The common extremalities in biology and physics maximum energy dissipation principle in chemistry biology physics and evolution

The Common Extremalities in Biology and Physics


The Common Extremalities
in Biology and Physics
Maximum Energy Dissipation Principle
in Chemistry, Biology, Physics and
Evolution

Second Edition
Adam Moroz

De Montfort University
Leicester, UK

AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS
SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
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Elsevier
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First edition by the Publishing House of the Ministry of Economy of the Belarusian Republic
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Second edition 2012
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Preface

The science of living nature is known as biology. Biology, in the modern sense of
the word, encompasses the entire hierarchy of life from the atomic-molecular level
to the global biogeocenosis. Furthermore, biology also formulates all temporal laws
of relationships in this complicated and, indeed, trophic hierarchy. In other words,
biology formulates evolution since life is not only a form of existence but also, in a
sense, a triumphal progression towards perfection.
Nevertheless, biology does not provide a satisfactory explanation for the origin
of life. How do we account for the emergence of biological processes in this
immense universe of dust, stars, planets and vacuum? Is it merely down to random
chance? Or, if life is not accidental, what does this signify? Biology does not
explain the transition from inorganic objects to organic life perhaps because the
reasons are too broad to be understood in purely biological terms. Moreover, the

concept of evolution has infiltrated and now permeates physics, that other ancient
vision of mankind and nature. A complex question arises: to which laws does life
owe its existence? Essentially, the answer lies partially within the realm of
physicsÀa science which is fundamentally concerned with non-living natureÀand
partially within the realm of biology. It seems that the answer to this question leads
to a deep unity between physics and biology.
A non-evolutionary theory of the origin of life (‘the Creation’) centres on the
involvement of a ‘super-essence’ (a super-individuality or a super-civilisation)
responsible for kick-starting the processes on Earth into life. The theory is reliant
on the inevitable and necessary emergence of the ‘super-essence’, preceded by the
appearance of primitive or increasingly sophisticated beings in nature at intermediate stages. Therefore the question of the origin of life can be reformulated in various ways: To what extent do the laws of inorganic nature and of physics derive
from, produce and require the emergence of biological processes? Is it possible to
deduce biological laws from physical and chemical laws? How do we define the
relationships between physical and biological processes? According to which law
are physical processes transformed into biological processes? To what degree are
biological regularities governed by physical regularities? Success in answering
these questions, even at an elementary level, might well enable the development of
a conceptual methodology that would generate biological laws based on physical
laws. Physics and biology would, then, be united by a uniform concept resulting in
a scientific ideology more accurately reflecting the interconnectivity of nature.
Therefore, this work represents an attempt to evaluate the feasibility of such a
mode of thinking that could be considered to allow some additional steps on the
path to better understanding the relationship between biotic and physical processes.


xii

Preface

However, one should note that any concept about nature, whether a simple mental picture or a complex formal mathematical scheme, is only one of many models

relating to matter. Concepts such as these are produced within the social forms of
informational mapping, cognition or information reflection. Mathematical science
(including the theory of models and the theory of systems) is itself merely one
form of information reflection, mapping and modelling. It can be characterised by
a dissociation from the material world (from supporting material messengers and
processes), creating an ideal, almost spiritual, models, and sometimes could be
thought that nature itself moves according to these models.
Nevertheless, mathematics, though eloquent in its description of nature, is simply a tool. It minimises the materiality of biosocial informational mapping systems,
creating sophisticated matter-less models of nature to a somewhat abstract level.
One can say that these mathematical models are the most formalised of models and
have the most information and functional capacity per least structural-energy cost.
This is one reason for the high efficiency of mathematical modelling. And yet, it is
an idealisation that could be considered to be rather two-dimensional “paper” form
and recently appears to have taken on a distinctly electronic character.
It is well known that the formal mathematical modeling has achieved the greatest success in explanation, description, and the forecasting of physical phenomena,
as well as in formal reconstruction of processes that take place within physical systems. At the highest level, the description of physical systems and processes proceeds from an extreme ideology to enable the formal mapping of physical
interaction or dynamics. This ideology is based on the least action principle
employing the variational method. The methodology of this approach contains the
following stages:
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There is a physical value called the action, which has the dimensional representation of
the product of energy by time.
The action, set as some value on all possible motions of a system, aims at minimum value

at any rather small interval of movement of a system.
From the principle using variational technique, one can obtain equations of movement of
a physical system (the EulerÀLagrange equations).
The trajectories, or the laws of movement of the system, can be obtained from the
EulerÀLagrange equations.

As follows from the first stage above, as early as the highest level of formalism,
physical modeling implies the energy sense of physical interaction and, as it turns
out, physical evolution. It is only at the final stage of the modeling process that the
outcome appears as a purely kinematical result—the movement trajectories. The
last stage also represents another sort of system behavior model—a model of states
of a physical system, on which it is possible to forecast the behavior of a real
system.
From this point of view, the formal mathematical description in biology has significant methodological difference, possibly a halfway policy. Here one can initially proceed from concepts and terms of a dynamic system (also of some formal
design), and in the majority of classical cases, from a system of differential


Preface

xiii

equations and hybrid systems for more complex models. The solution of such a
system represents the law of movement or trajectory, providing information on the
location of a real system at any moment of time in the multidimensional phase
space of parameters of a biological system.
We shall note that in contrast to the physical way of formal modeling, the energetic sense, as the most formalized scheme of phenomena occurring in a biological
system, escapes. However, this sense, indeed, is well verified by the whole logic of
physical formalism, and this sense in itself is not less important in the conception
of the nature of biological phenomena.
This argument proceeds from the suggestion that it is the energy sense that can

initiate the level of formalism, similar to top-level variational formalism in physical
description, and consequently, it is ideology of a common and unified approach in
biology and physics.
In connection with the above, it is important to look at the most common energy
laws of biological phenomena (which, in fact, are the thermodynamic laws) in
order to mathematically formalize, with the purpose of development on the basis of
these laws, a universal, informative, and formal scheme generalizing the laws of
biology. We expect that such ideas could result in a formalism, similar to variational formalism in physics, and that it could be a basis for the ideological unification of biology and physics.
One may also bring to mind that the determining difference of biotic processes
is that they carry out the utilization or dissipation of energy, with the qualitatively
irreversible transformation of free energy to the thermal form. It is this that hinders
a direct introduction of the ideology of the least action principle into biology and
in biological kinetics.
Therefore, we could initially consider the interpretation of the variational
approach with reference to the processes with explicit dissipation, i.e., to relaxation
processes in chemical and biological kinetics.
In this connection, it is expedient to reflect on the energy sense of the phenomena
related to these areas, i.e., the hidden dynamic reason of one or another biological
processes and the form of their representation (mapping) in the corresponding
formal models. In a sense, it would be similar to the solution of the reverse problem
of variational calculus for biological kinetics—when the variational function of the
corresponding under-integral function, the Lagrange function, needs to be found
from the equations of motion, from a dynamic system or a system of differential
equations. The solution of such a problem would enable us to analyze in an explicit
form the energy properties of the phenomena initially presented within the parameters of a dynamic system. However, the reverse variational problem could be
solved for a very limited range of cases, and there is little optimism about finding
the successful solution as far as biokinetics is concerned.
Thus, it is possible to follow two different approaches in the formal mathematical and deterministic descriptions of these rather opposite groups of phenomena—
biology and physics. The first is related to physics, with an explicit energy sense
outgoing from energy properties of the physical phenomena, from the least action

principle, leading through the EulerÀLagrange equations to the laws of motion or


xiv

Preface

trajectories. And the second, more widespread in biology, likely begins with a comparison of a physical description, directly from so-called dynamic models, of the
systems of differential or other kinds of equations, and it finally results in the same
stage—the laws of motion, or trajectories.
We expected that the mutual penetration of both approaches could to a great
extent promote mutual development as well as the technical and ideological enrichment of physics and biology.
We shall emphasize that the undertaken consideration concerns rather classical
models—the models presented by systems of differential equations; however, even
such a phenomenological consideration is difficult to implement consecutively within
the frameworks of these two broad and opposing phenomena—the biological and the
physical.


1 Extreme Energy Dissipation
1.1

Hierarchy of the Energy Transformation

1.1.1 Thermodynamics—A Science That Connects Physics and Biology
The general laws connecting biology and physics are particularly related to energy
transformations, since thermodynamics is the phenomenological science that describes
the energetical macroscopic characteristics of systems. Thermodynamics, which directly relates to biology, is known as biological thermodynamics. It covers subjects connected to the interconversions of different forms of energy, ranging from those in the
simplest chemical reactions and ending with energy complex trophic changes of the
biomass of different species. The energy and structure conversions in these complex

changes eventually end and, can be saying in a different way, transfer to another quality in the large number of social processes.
Evolutionary and methodologically biological thermodynamics begins with the
thermodynamics of chemical reactions. The latter are known to have produced a
huge variety of far from equilibrium (and also from steady state) phase-separated
biochemical systems, which are actually biotic cells. One can, therefore, imply that
the thermodynamic (energetical transformation) laws of biology begin with the
thermodynamic laws of chemical reactions. The study of these laws is termed
chemical kinetics. For example, the thermodynamic fluxes are the velocities of
chemical reactions, and chemical forces are no more than the affinity for chemical
reactions. It is, therefore, evident that the subjects of chemical thermodynamics and
chemical kinetics overlap to a large extent.
One can also say that biotic organisms are complex, phase-separated, chemical
reactions that contain very specific molecular forms of informational support
processes. It can be said that these reactions, in the process of evolution, have
allowed organisms to acquire not only mechanical but also the development of
more complex high-adaptive degrees of freedom—informational. On some stages
of the evolution, these complex reactions significantly enhanced the role of thermodynamic regulatory feedback loops, regulating for instance the heat balance
in the process of cellular respiration or maintaining the temperature of the body
and so on.
However, thermodynamic systems operate with some characteristics that reflect
the hierarchy of the physical quantities in the process of energy transformation.
Biological thermodynamics, in turn, mirrors the hierarchy of the complex biological world. It is, therefore, useful to remind ourselves of the construction of the
The Common Extremalities in Biology and Physics. DOI: 10.1016/B978-0-12-385187-1.00001-0
© 2012 Elsevier Inc. All rights reserved.


2

The Common Extremalities in Biology and Physics

hierarchal thermodynamic terms and the definition of these with respect to the
crucial differences in the organizational hierarchy—a central point in the difference
between pure thermodynamic and biological phenomena.

1.1.2

Hierarchy of the Processes and Parameters in Thermodynamics

Thermodynamics is known as a phenomenological science. Thermodynamics represents a classical and historical example of a macroscopic description of the energetic
transformations in various macrosystems. However, it is important to note that the
understanding of macroscopic and particularly microscopic phenomena has steadily
been changing with time.
Thermodynamics, as we know, deals with the systems containing a large number
of particles (around 1010À1030). As we mentioned, such macroscopic systems can
be characterized by two kinds of variables:
1. Macroscopic parameters—characterizing the system in relation to the neighboring macroscopic world, or the system as a whole. Two classic examples of these variables are volume and pressure.
2. Microscopic parameters—characterizing the properties of the particles that make up the
system (mass of the particles, their velocities, momenta, and so on). Now, it seems obvious that in any study of processes and systems, it is possible to set at least two fundamentally different edge levels for these processes, i.e., macroscopic and microscopic levels.
The former is known as the phenomenological level, which can be heavily characterized
by thermodynamics.

Let us note, therefore, that the concept of a thermodynamic system, as studied in
thermodynamics, is more complicated than the concept of a mechanical system,
due to the dynamic nature of the values at both of these levels. Clearly, these two
levels of variables are interrelated, although they have their own dynamism. The
inconvenience of describing a one level (macro), which employs the microscopic
description of the states of all components of a system of microparticles that carry
the microscopic parameters, leads to a statistical interpretation of these quantities,
which connects them to the macroscopic parameters. The fundamental relationships
involved are closely related to thermodynamics—a form of statistical mechanics.

Thermodynamic consideration deals only with the macroscopic parameters of the
systems, i.e., those of clear phenomenological character.
Therefore, the distinctive feature of thermodynamics (as a phenomenological,
macroscopic description) relative to mechanics (microscopic description) is that for
the thermodynamic systems the concept of two types of processes is considered.
In some sense, thermodynamics is the first hierarchical science within physics. If in
mechanics the reversible character of processes is the rule, and the irreversibility
in some way is an exception, in thermodynamics, perhaps, reversibility of processes is
the exception, and irreversibility is the rule. Thermodynamics, therefore, requires
specific fundamental law to take account of its macroscopic nature—the second law
of thermodynamics. The apparent dominance of irreversible processes in the macroworld is associated with the peculiarity of the dynamic nature of the relationship of


Extreme Energy Dissipation

3

microstates and macrostates of the thermodynamic system. Reversible processes are
understood as taking place in such a way that all the macroscopic parameters can be
changed in the opposite direction, without any other macroscopic changes, even outside the system. The irreversible processes occur so that they can run in the opposite
direction, just when connected with other macroscopic changes, such as the environment. Reversibility and irreversibility, which manifest themselves macroscopically,
are closely linked with the microscopic characteristics of particles, i.e., their own
dynamism. Due to the dynamic nature of these macroparameters and the large range
of energy that characterizes (changes/transformations) the system, these values have a
certain hierarchy.

1.1.3

Macroparameters: Energy and the Forms of Its Exchange

In consideration of the physical interactions in thermodynamics, the nature of interaction is explicitly emphasized as the exchange of energy through two distinct
processes—it is the result of work or heat transfer. However, as we mentioned in
thermodynamics, there are two levels of hierarchical processes—the microscopic
and macroscopic. These and, therefore, the energy exchange (or thus, the interaction) involved in thermodynamics are different and have the appropriate hierarchy.
Energy, traditionally, is distinguished in several forms.
The internal energy of a system takes all the available energy into account, without regard to the hierarchy of interactions at the macrolevel or microlevel. This
energy includes the energy of all microscopic particles, at all levels of the hierarchy
of the system, and includes the energy of all known interactions between them, as
well as the macroscopic part of energy (related to the system macroparameters, like
pressure, volume). It should be emphasized that because of this broad concept of
internal energy, it is impossible to establish its full value for any system, because it
includes a large number of constituents that are difficult to take into account.
Therefore, we often deal only with the change in internal energy of the system
between any of the states of the system.
Heat, also referred to as thermal energy, is the kinetic energy of the microparticles that make up the system. This energy is transmitted through the exchange of
the microscopic kinetic energy of the microparticles during their collisions.
Therefore, thermal energy (heat) has macroscopic properties due to the large numbers of particles involved in the kinetic motion and the large amount of transferred
energy. This type of energy exchange is not linked to the exchange of the energy
of a system in the process of work.
Because nonequilibrium states are characteristic of macrosystems, the energy in
thermodynamics acquires one other property. The energy can also be considered as
a measure that characterizes the aspiration of processes and systems to reach their
equilibrium. In other words, it can be considered as the measure of the relationship
between the relatively nonequilibrium degrees of freedom and the equilibrium.
In a certain sense, the nonequilibrated degrees of freedom can be interpreted
as overcrowded by motion. To some extent, the energy is a measure of the overflow by the motion of degrees of freedom (a measure of the nonequilibrium


4

The Common Extremalities in Biology and Physics

structural state). Therefore, the apparent micro- and macrodifferentiation dominates
when considering the hierarchy of forms of energy in thermodynamics.

1.1.4

Macroparameters: Heat as a Nonmechanical Method to Change
the Macrostate of Thermodynamic Systems

Thermodynamics, in the first instance, studies the range of phenomena that are related
to heat (thermal heat). Heat, the thermal energy Q, is primarily a macroscopic materialization of the mechanical motion of a large number of microparticles. Actually, the
energy of this motion is characterized as thermal energy.
Paradoxically, heat is a macroscopic manifestation of microscopic changes, and at
the same time, it is a microscopic form of energy exchange, having a macroscopic
effect. However, it should be more rigorously understood that heat is the microscopic
form of energy transfer that is related to the change of macroscopic parameters, like
temperature, which has both a macroscopic and microscopic sense. Therefore, heat
transfer is only a microscopic form of change in internal energy.
The temperature reflects the macroscopic manifestation of the intensity of the
microscopic motion. Temperature is the molar heat of the kinetic energy per one
mechanical degree of freedom. Therefore, heat energy is transmitted at the microscopic level and not directly related to the macroscopic work.

1.1.5

Macroparameters: Physical Work as a Pure Mechanical Way to
Change Macroparameters

Work looks like it is in opposition to heat: It is a way to change the internal energy
of a macrosystem, the method of transmitting of energy in a process, when the

transfer process is directly related to the change of macroscopic parameters.
The concept of work in thermodynamics comes from mechanics. In mechanics,
the elementary work is the product of force on the small displacement:
δA 5 F dl:

ð1:1Þ

It should be noted that the elementary work, even in mechanics, is not, generally
speaking, the exact differential of any function of the displacement l, and, therefore,
at the designation of its elementary value employed δA, and the sign of the elementary
change is not used [1,2]. It is also important because the work is not a measure or
function of the state, but is only a measure of processes, a quantitative measure of the
energy exchange in a process. Work is a function of the process not the state.
In a simple example of the thermodynamic case for an ideal gas, work is equal
to the product
δA 5 F dV:

ð1:2Þ

It should be emphasized that in thermodynamics, work is also not an exact differential of any function of the state, but work is a function of the process [2,3].


Extreme Energy Dissipation

5

The formal property of this underscores the fact that the work is a process, there is
a means of energy transfer, and it is not a function of state. On the other hand,
work is a quantitative measure of energy transfer into the system through the action
on it of some generalized forces from other systems.

1.1.6

Macroparameters: The Energy Conservation Law

The first law of thermodynamics imposes the quantitative relationship for the transformations between the macroscopic and microscopic forms of energy (in a wide
sense between the qualitatively different degrees of freedom of physical motion) to
another. Formally, this is the postulation of the existence of an additive value—the
internal energy of the system.
The change in the internal energy of a system is equal to the sum of the heat
into the system and the work done on the system, which is formally expressed as:
dE 5 δQ 1 δA;

ð1:3Þ

where dE is change in the internal energy of the system, δQ is the amount of thermal energy supply to the system to heat the microscopic degrees of freedom, and
δA is the work done on the system or the amount of energy that the system gained
by the “nonthermal” macroscopic degrees of freedom.
The first law of thermodynamics strictly delineates the possibility of different kinds
of energy in relation to the processes in which the system participates. These processes are the microscopic and macroscopic forms of energy transfer: heat and work.
Actually, this is a distinction in the microscopic and macroscopic aspect, as heat and
work do, in this sense, belong to different levels of this two-leveled hierarchy.
The first law of thermodynamics does not discriminate between the macrodegrees
and microdegrees of freedom, or the interaction between systems. This interaction
depends on the hierarchical affiliation, which, as it turns out, is related to reversibility
or irreversibility of the interaction process of energy exchange. It should be emphasized that this question arises only in thermodynamics. In mechanics, its emergence
does not manifest itself so clearly. It is the second law of thermodynamics that raises
the question of the status of energy as a measure of reversibility/equilibrity. The first
law discriminates between the ways of energy exchange, in terms of thermal and nonthermal, and, naturally, states that the overall energy in their forms is conserved.
However, even if the macroscopic parameters remain constant, changes may

occur at the microscopic level. This leads to the fact that for the same macrostate,
the system can have multiple sets (numbers) of microstates that can be different in
the sense of stability. This last fact leads to the second law of thermodynamics.

1.1.7

Macroparameters: Free Energy—Macroscopic Measure
of Nonequilibrium

We can say that the thermodynamic study of the interaction of qualitatively different macroscopic degrees of freedom is an investigation of the redistribution of


6

The Common Extremalities in Biology and Physics

energy among the various structural and energetic macrostates. These macrostates
represent the degree of freedom in the system, during its interaction with the environment or another system. This sense of imbalance (in the sense of equilibrium)
in all degrees of freedom of the system, regardless of the inflow of external imbalance, or an existing imbalance in the system, manifests itself according to the second law of thermodynamics, as a more or less equilibrated state. More specifically,
macroscopic forms of energy (related to microscopic degrees of freedom and
macrostates) are divided into thermal and nonthermal. This division is a characteristic feature, the basis for thermodynamics, and its main laws define the relationship between all forms of energy, in accordance with this division.
In line with this interpretation of micro and macro forms of energy, the internal
energy of a system can be qualitatively divided into the relationship between the possibilities of its transformation into the macroscopically ordered form of energy—work
(particularly into mechanical work). This part of the internal energy that can be converted into any type of work—mechanical, chemical, electrical—can be defined as
free energy. Another part of the internal energy, which cannot be converted into macroscopic work (as was already mentioned), is referred to as the bounded energy and is
usually associated in thermodynamics with the energy of the thermal motion of particles that make up the thermodynamic system.

1.1.8

Macroparameters: Universal Fatality of the Processes—The Second

Law of Thermodynamics and the Hierarchy of Energy

The second law of thermodynamics reveals the properties of reversibility/stability
or irreversibility/instability of a process of interaction of one or another degree of
freedom or that of another way of energy exchange. It reveals the reaction of the
system, describes a macroscopic interaction as a way to change the nonequilibrity,
and highlights the special status of the thermal degree of freedom as the most equilibrated (stable one), thereby selecting the thermal energy, both qualitatively and
quantitatively. The second law underscores the crucial irreversibility of the thermodynamics of all processes of energy conversion and directs this irreversibility to
the thermal degree of freedom as the most sustainable energy form. In terms of the
relationships between the microscopic and macroscopic states of the system, the
second law, to some extent, subordinates the status of macrostates to only a certain
set of microstates.
It is the second law of thermodynamics that from a formal point of view allows
us to introduce a macroscopic function: entropy S. The feature of this function is
related to the spectrum of microstates. It is postulated that this function cannot
decrease with time for a closed system.
Pure thermodynamical, or phenomenological, entropy is introduced by the ratio
of elementary change in the heat transfer into the system, δQ, to the absolute temperature T at which this increment happened:
dS 5

δQ
;
T

ð1:4Þ


Extreme Energy Dissipation

7

where S is entropy. However, this introduction implies a reversible process of heat
transfer.
For an irreversible process,
dS .

δQ
:
T

ð1:5Þ

This means that there is an irreversible process of so-called dissipation of free
energy, when there is some gain of entropy that did not come from heat, but which
is also converted into the energy of the thermal motion of the particles. Therefore,
the effective dS was greater than that in the case of the reversible process.
This additional increase in dS reflects the fact that other types of energy are
transformed so that the energy of thermal motion increases. It is, therefore, why
entropy is a parameter that characterizes the relationship to qualitatively define different degrees of freedom and their energy with the enormous reservoir of an
energy absorber, which is their thermal degree of freedom.

1.1.9

Macroparameters: Helmholtz Free Energy

In an isothermal reversible process, when the system temperature does not change,
taking into account Eq. (1.4), the work done on the system (1.3) can be represented as:
δA 5 dE 2 δQ 5 dE 2 T dS 5 dðE 2 TSÞ:

ð1:6Þ

We can then define for systems at constant temperature and volume,
δA 5 dF;

ð1:7Þ

where F 5 E 2 TS. The value F is referred to as the Helmholtz free energy [3]. It
should be emphasized, again, that our interest in free energy is associated with its
role in providing energetical support for life processes.

1.1.10 Macroparameters: Enthalpy
For real systems and processes, it must constantly be borne in mind that these systems have volume and are under, sometimes constant, atmospheric pressure—i.e.,
the redistribution of energy is constantly followed by some mechanical work.
Partly because of this, another function of the state, enthalpy H, is widely used.
Taking into account the change in internal energy E and the change in volume V
and pressure P, one can write enthalpy as:
H 5 E 1 PV:

ð1:8Þ

In general, an elementary change in enthalpy dH, when under changing volume
V and pressure P, can be expressed as:
dH 5 dE 1 P dV 1 V dP:

ð1:9Þ


8

The Common Extremalities in Biology and Physics

The introduction of enthalpy can take into account the part of energy that can be
converted into mechanical macroscopic work.
In thermodynamics, it is common to introduce another state function, Gibbs free
energy G, which is defined as:
G 5 H 2 TS;

ð1:10Þ

where H is enthalpy, S is entropy, and T is absolute temperature, which takes
into account the real state of the macroscopic system under constant temperature and pressure P. Gibbs free energy is useful in the description of chemical
processes, and when under experimental conditions the pressure is usually
constant.
If energy exchange occurs at a constant temperature, the change in Gibbs free
energy is expressed as:
dG 5 dH 2 T dS:

ð1:11Þ

It should be noted that for a certain process, the overall difference Δ is
ΔG 5 0:

ð1:12Þ

Then the system is in equilibrium. If for the ongoing process
ΔG . 0;

ð1:13Þ

this means that there is a gain, a surplus of free energy in the process, and it cannot

proceed spontaneously. If for the ongoing process
ΔG , 0;

ð1:14Þ

this is the criterion for spontaneous processes. The system then has the ability to
perform work.
This does not mean that the total quantity of ΔG can be converted into work,
ΔG—a measure of the maximum possible work that can be obtained from the system. It is the second law of thermodynamics that states that not all the amount of
ΔG can be transformed into work, but only a certain part. The total value of ΔG
can be converted only in the case of a reversible process. If all of ΔG can be converted into work, we could revert to this kind of ΔG term in its original form. So,
based on the second law of thermodynamics, ΔG can be only partially converted
into mechanical macroscopic work.

1.1.11 Link from Macro- to Microparameters: Physical Entropy
As noted previously, when considering thermodynamic systems, i.e., the systems
consisting of a large number of particles, we must take into account that there are


Extreme Energy Dissipation

9

few levels of monitoring of the physical system and so two kinds of quantities
characterizing the system. One of the monitoring levels is at the macrolevel
which characterizes the system macroscopically. This is represented by the values
of volume, pressure, internal energy, and so on. The second level is the microlevel of
observations with microparameters—coordinates and momenta of the particles,
and so on. It is clear that because of the identity and indistinguishability of the microparticles comprising the system, any macroscopic state that is represented by a large
number of microstates is ambiguous. Therefore, a simple question is logical in this

sense: how many microstates are represented by a macrolevel state, i.e., by a given
state within this macroscopic system? This number could be treated as the degree of
degeneration of the macroscopic level, with the given values of the macroparameters,
which can be designated as W. Because this number is very large, a logarithmic measure is used. According to Boltzmann (see, for instance, Refs. [4,5]), this introduces
the value
S 5 kUln W;

ð1:15Þ

where k is the Boltzmann constant, W is degeneration of the macroscopic state, or
the number of microstates consistent with the given macrostate, the number of
microstates that represented this given macroscopic state. The value of S is usually
called the physical (Boltzmann) entropy. Entropy, therefore, acts as a quantitative
measure of the uncertainty governing which microstates are responsible for the
observed macroscopic state.
It should be noted that there is an informational nuance of physical entropy: S is
a measure of the uncertainty about which microstate of the system is responsible
for a macrostate with a given energy.
The physical meaning of above definition of entropy lies in the fact that the
number of macroscopic states of the system and the number of microscopic states
of the system are different. Moreover, the number of microstates of the system is
so many orders of magnitude greater than the number of macrostates. It therefore
makes sense to introduce a logarithmic measure of the representability of a macroscopic number of microstates.
It can also be stated that entropy is a measure of disorder in the system. Indeed,
the larger is the degeneration of the system’s energy state, the higher the microscopic
disorder and the greater the entropy of this state. However, what might happen if the
particles are physically impossible to move—if they are not so indistinguishable, at
least in a spatial sense? Then each macroscopic state has a unique microstate. Then
W 5 1 and S 5 0. In this case, the entropy description of systems does not work well.
When the system is highly personalized, the concept of entropy makes enough sense.

Then the energy characteristics of the system seem to be more constructive. Entropy
is, therefore, likely to “depersonalize/dehumanize” the world and make the system
faceless.
Final note: Entropy is good when the microlevel degrees of freedom (states) can
be easily counted. That is, ideally, when it is just one microlevel degree of freedom
and all the probabilities can be easily calculated.


10

The Common Extremalities in Biology and Physics

1.1.12 Microparameters: Statistical Interpretation of Free Energy
and Entropy
Statistical mechanics offers another possible interpretation of entropy, associated
directly with the distribution of the probability of finding the system in the microstate at the realization of a particular macrostate. This leads to the following definition of entropy:
S52

N
X

pi Uln pi ;

ð1:16Þ

i51

where pi is the probability of finding the system in microstate i.
However, this microstate can be characterized by a certain energy: The probability of pi microstates are associated with this energy in a certain way. This dependence was first obtained by Gibbs in 1901 and is called the Gibbs distribution (see,
for example, Ref. [6]) or the canonical distribution:

 
Ei
;
ð1:17Þ
pi 5 C exp 2
T
where C is a normalization constant, and


N
X
1
Ei
:
5
exp 2
T
C
i51

ð1:18Þ

It can be found that free energy is linked to the Gibbs distribution. Substituting
in the formula for the distribution of entropy, we then obtain


N
1X
Ei
E

5 2ln C 1
Ei exp 2
S 5 2ln C 1
T
T i51
T
or
ln C 5

E 2 TS
:
T

ð1:19Þ

The average energy E can be defined as the internal energy E, so
E 2 TS  F;

ð1:20Þ

where F is Helmholtz free energy (see, Eq. (1.7)). Then,
F 5 T ln C 5 2T ln

N
X
i51

exp

 

Ei
;
T

where C is the normalization constant in the Gibbs distribution.

ð1:21Þ


Extreme Energy Dissipation

11

Therefore, free energy can be expressed as a measure related to the deviation of
the actual energy distribution from the most natural; in some sense, optimal for
these macroconditions. There are a number of other definitions of entropy. The
most well known is the Tsallis entropy [7], which is a generalization of
BoltzmannÀGibbs entropy. However, all of these are based on the accountability
of probabilities of microstates in a two-leveled thermodynamic model: the microstate and the macrostate. In actual fact, the hierarchy of biological systems is much
more complex.

1.1.13 The Removal of Energetical Nonequilibrium and the Entropy
Production
The process of irreversible transformation of energy from unequilibrated forms, in
some sense unstable material forms, to the more equilibrated, stable forms, is the
process of increasing entropy. It is called the energy dissipation or the entropy
production.
The full balance of the elementary changes of thermodynamic quantities (potentials) is given by the Gibbs equation, which for the case of small deviations from
equilibrium appears as (see, for example, Prigogine [8À12]):
T dS 5 dE 1 p dV 2

N
X

μi Udmi ;

ð1:22Þ

i51

where E is internal energy, p is pressure, μi is the chemical potential per mass unit,
and dmi is an elementary change in the mass of ith component. The Gibbs formula,
therefore, links the change in entropy in the system with the change of potentials,
in particular the free energy, indicating that at an increase in entropy in the system
free energy dissipates.
If the change in internal energy dE 5 0, one can express the elementary entropy
in the system as the sum
N
1X
μ Udmi 1 p dV;
dS 5 2
T i51 i

ð1:23Þ

or generalizing
N
1X
Ji UdXi ;
dS 5 2

T i51

ð1:24Þ

where X is generalized thermodynamic forces and J is generalized thermodynamic
flows. Introduction of entropy production in this manner allows the general form to
formulate the entropy production, which is convenient when considering nonisothermal processes.


12

The Common Extremalities in Biology and Physics

The production of entropy P in a closed system can be defined as:
dS
5
P5
dt

ð
σUdV;

ð1:25Þ

V

where σ is the density of entropy production or the so-called dissipation function.
The density of entropy production σ in a closed system can be written [10] in
terms of the values of generalized thermodynamic forces X and J fluxes by the following equation:
σ5

N
X

J i UXi ;

ð1:26Þ

i51

where X is generalized thermodynamic forces that initiate the irreversible processes
in the system and J is generalized thermodynamic flows that implement these processes and address the imbalance.
One can say that the hierarchical sense of the second law is that small and
reversible changes at the microscopic level produce irreversible changes at the
macroscopic level.

1.1.14 Dissipation in Chemical Transformations
In this study, we consider chemical kinetics as having been closely related to biological kinetics and which, in some sense, even generates biological kinetics. It
will, therefore, be a good example to consider entropy production, or energy dissipation, during chemical reactions, because it is such a dissipation that causes life
processes. In addition, it can be largely argued that chemical kinetics is a convenient example, because the microparameters coincide with the macroparameters,
and at the level of biokinetic microparameters, the processes become even biological (specific to the kinetics of species densities, ecological kinetics).
An example of the generalized thermodynamic forces, which lead to imbalances
in the case of chemical nonequilibrium, is the affinity of a chemical reaction,
divided by absolute temperature T [12]:
Xl 5

Al
:
T

ð1:27Þ

Accordingly, the generalized thermodynamic fluxes Jl, eliminating this chemical
imbalance, are associated with the chemical reaction rates, and can be written in
terms of the so-called extent coordinates of the chemical reactions ξl:
Jl 5 ξ_ l ;

ð1:28Þ

where ξ_ l is the velocity of the lth chemical reaction and ξ l is the coordinate of the
lth reaction, or extent from equilibrium.


Extreme Energy Dissipation

13

The extent coordinates from equilibrium ξ l, participated in the expression for the
generalized thermodynamic flows (1.28), are related to the concentrations of any
involved in the lth reaction of substance xi in the stoichiometric ratio ν li as:
xi 5

X

ν li ξl ;

ð1:29Þ

l

or in vector
xT 5 Nξ;

ð1:30Þ

where x is the vector of concentrations, N is the stoichiometric matrix with elements ν li, and ξ is the vector of independent extends [13]. Then the vector of generalized thermodynamic fluxes J will be
T
_ 2T ;
J 5 ξ_ 5 xN

ð1:31Þ

where ξ_ is the vector of rates and N2 T is the inverted transposed matrix of stoichiometric coefficients. Then the density of entropy production (1.26) in such a system
of l independent reactions can be written in a vector form as:
_ 2T X:
σ 5 xN

ð1:32Þ

We should note that the total change in entropy in an open system is composed of
the entropy production inside the system and the flow of entropy into the system.
It is not possible to impose any general principle, including the extreme
demands on the production of entropy (ever-increasing according to the second
law of thermodynamics), at least within the system, when this increase is the only
possible process. It should be emphasized that other processes are, from an entropic standpoint, only minor details. However, in terms of the degree of reaction
and their derivatives, they are also the very faceless looking kinetics of these
reactions. Maybe for more interpretable processes associated with changes in the
mechanisms, we should initially work directly with the concentrations and their
derivatives.

1.1.15 Dissipation of Nonequilibrium in Open Systems
Often one uses the following purely thermodynamic classification of thermodynamic systems as:
●

●

●

isolated—isolated from the environment, which do not share any substance or energy;
closed—exchange energy;
open—exchange energy and matter.

It is believed that systems are in steady state or equilibrium if they do not
change with time in the macroscopic state.


14

The Common Extremalities in Biology and Physics

The description of the dissipative processes in open thermodynamic systems has
often had a tendency to interpret the entropy due to the fact that most of the processes do not necessarily occur at a constant temperature. The rate of increase in
entropy in an open system can be divided as follows [10À12]:
dS 5 dSext 1 dSint ;

ð1:33Þ

where dSext is the inflow of entropy from the outside and dSint is the entropy production inside the system. However, it should again be noted that it is difficult, in
terms of entropy, to describe the large number of unique processes of energy and a
structure’s conversion that takes place, even in relatively simple chemical systems;

this is even more difficult to do so in biochemical or ecological/biocenotical
kinetics.
In this sense, the energyÀstructural description has a large variety and potential
and can be more adequate than an entropic description. Therefore, paying tribute to
the entropical description, the energyÀstructural description in terms of the irreversible transformation of energy and its structural forms should be considered as
for the processes taking place in any isolated systems, as well as in the open systems. This should be done in view of the fact that entropy is only a measure of the
ambiguity/uncertainty of the macroscopic state with certain energy; it is a measure
of the representability of the macrostate by a set of microstates.
Because the chemical processes of generalized flows can always be expressed in
terms of reaction rate (and, hence, a derivative of concentration), it makes sense to
directly address the kinetics of entropy production, or dissipation of energy in terms
of concentrations and their derivatives. This would also facilitate a clearer interpretation of the mechanisms of chemical processes themselves, since these mechanisms are usually expressed in terms of dynamical systems. The close relationship
with the mechanisms would allow one to consider the ways of energy conversion
in the formulation of the variational problem. For the latter, it would be of no small
importance compared with the mechanics, where the description is also made in
terms of coordinates and derivatives.

1.1.16 Energy Dissipation or Entropy Production—The Energy Picture
Can Play a Role
So do some processes only become clear when the production of entropy is considered within the system itself? In terms of entropy, this aspect has the physical meaning of the design review processes. It is known that the entropy representation is
useful in analyzing nonisothermal processes. But entropy is statistically significant
only as a measure of the representability of the macrostate from a number of microstates. It is only a measure of the degeneration of the macrostate of the system, the
logarithm of the number of microstates responsible for a given energy state. What is
the point of assuming such a case—the flow of degeneration of the state from
outside? And from what material structural state is this degeneration imported?


Extreme Energy Dissipation

15

From the very interpretation of entropy, it can be seen that it is a somewhat
simplified description of the exchange of energy and structure. This is particularly
true in the case of biotic systems. Real substances produce effects such as smell.
Maybe biotic systems reveal their sources of food by the smell of entropy? What
functional distinction in language is there between the entropy of a lysozyme and
ribonuclease?
Perhaps this might be, in this sense, a purely energetic description of a much
more detailed fact. For example, the spectral (and, therefore, energetical) description of the proteins in the nuclear magnetic resonance (NMR) spectral region shows
huge differences between the proteins. Moreover, the energetical description is
closely related to the structure, and from the energy-structural representability perspective, this has much more diversity than entropy. Moreover, in cases of entropic
description, the structure is not represented at all and, in some sense, the whole
nature in terms of it (entropy) is just one face—the face (and maybe more appropriate, the shadow) of the degeneration of the macrostates.
Therefore, it makes even more sense to consider the processes in isolated systems, as well as in open systems, as the irreversible transformation of energy and
structure. Moreover, when one considers the dissipation of free energy, it is easier
to observe this dissipation, for example, by the spectroscopic method. If we recall
the interpretation of entropy as a shadow of energy, following F. Wald (see, for
example, Ref. [14]), the monitoring of the reality by its shadow, if not meager,
may present the result.
In some sense, entropy is only a consequence of the representability of a macrostate
by the microstates, the result of some “democracy” on the microlevel. Therefore, this
work seems more impressive by the diversity in nature of the faces of energy: a structural, rather than an entropy-based description of the processes. Entropy still fascinates, but this does not deny the huge role of energy. Moreover, it can be associated
with energy management, meaning the principle of least action. To us, it seems logical
to concentrate on an energetical representation for the reasons noted above. Let us
also note that the energetical character of our study stresses its phenomenological
nature.

1.1.17 Biological Hierarchy and Its Complexity
However, biological hierarchy is not as simple as in thermodynamics/statistics.
Biological hierarchy is much more complicated. The quantities and values displayed in the macroscopic biological world are not just the averages of some

microprocesses. The constituent microprocesses cannot be thought of as those having just one level of organization. The mean value is not so productive and moreover fails to represent microorganization at the microlevel. It seems that entropy,
as a thermodynamic and statistical definition, cannot fail in a proper quantitative
representation of order or disorder at the microlevel. The character of order/organization at the molecular level of biological processes is huge/unique. Its tremendous
nature is beyond the imagination and can sometimes be seen as higher than that at
the macrolevel. It is one of the reasons that make the applicability of entropy, in


16

The Common Extremalities in Biology and Physics

any definition, uncertain [5]. It is very difficult to reduce the microdescription to
the energetic description because different sorts of substances that are involved in
microprocesses are organized in different ways. One of the examples can be on the
cellular level of microscopic processes.
Hence, significant progress has been done in the field of complex systems
[15], one can also note that classical phenomenological, two-leveled thermodynamic-like, macroscopic description also has certain difficulties outside physics.
It does not work sufficiently well in biology, economics, or sociology. It works in
chemistry, where, in fact, a macroscopic description coincides with elementary
chemical kinetics (which is also a microscopic description). In more complicated
chemical systems, it has some limitations. However, taking into account the fact
that chemical kinetics is indeed formally linked to biological kinetic processes at
a molecular level (also evolutionary bioprocesses start at the chemical level), it
is a good reason to start the study of biological and physical descriptions with a
consideration of the chemical processes described. Therefore, in our study, we
concentrate at the phenomenological, e.g., the energetical description, keeping
also in mind that it is also limited.
As was mentioned, in contrast to the two-leveled thermodynamic-like model,
biological systems are characterized by multilevel, nonlinear interconnections.
Multilevel interpenetrating feedback results in a very complex system of regulation.

Due to the links between different biological layers, new functionalities emerge as
important life properties from this biological complexity. These can be characterized by self-organization, optimal adaptation, self-replication, and coevolution. In
general, biological systems are far from equilibrium due to the multiple control
loops needed to maintain the biological system in homeostasis.
A global hierarchical structure of biological processes can be represented by the
following sequence: ecosystem—species interdependence; animal populations—
competition and the food chain; individual organisms—physiological functioning;
limbs and physiological systems—organism homeostasis; tissues—growth, maintenance, and repair; cells—growth, specialization, and death; organelles—cell homeostasis; and biological macromolecules—folding, molecular recognition and binding.
The hierarchical structure and control in biological systems has developed
during a long period of evolution. The complexity of biological systems is required
to create new functionalities, which can be characterized as self-organization, optimal adaptation, self-replication, and coevolution. Many regulatory processes have a
dynamic and cyclical nature, manifesting themselves over different characteristic
time scales. Regulation in any biological system cannot be adequately understood
in the framework for any static two-leveled model (the simplest model from a
mathematical point of view). Behavioral control in a biological system should be
considered in the framework of a dynamical system approach. From a thermodynamic point of view, biological systems are too far from the equilibrium
state; therefore, only dynamical models can be used to investigate their complex
behavior. Many attempts to describe the informational processes in biosystems,
on the basis of entropy-informational principles, have failed—possibly because
biosystems are multileveled, autonomic, dissipative, and intelligent systems. Here


Extreme Energy Dissipation

17

we have adopted phenomenological methods for deriving nonlinear dynamical
models, which we will use in a study of regulatory processes in a multilayer
system.
Hierarchical regulation in multileveled biological systems has evolved to provide optimal adaptation and robustness. At the same time, biological systems have

acquired the energetic-structural resources for adaptation and competition. The proposed research will investigate these features of biological system behavior using
mathematical modeling with multilevel hierarchical feedbacks.

1.1.18 Some Conclusions
In light of above, thermodynamics is the simplest hierarchal model in physics. It
and its quantities and parameters describe the energetical, main properties of
change within physical systems on the macroscale. Statistical mechanics/thermodynamics is concerned with dealing with a microscopic description of the processes
in thermodynamic systems, i.e., the description of a thermodynamic system on the
microscale. It has its own terminology and complicated concepts, together with
methods to link microdescription with the macrodescription. One of the most powerful concepts in this link is the concept of entropy. The different ways to define
entropy are well developed for various physical systems within a mechanical vision
of their microstates. However, there are also some difficulties in the universal definition of entropy that can be applied to systems with a complex, nonÀtwo-level
hierarchy, such as biological systems. Consequently, the energetical laws and,
indeed, energetical properties of systems with a complex hierarchy can be considered as another optional framework in a phenomenological description that can
play a unification role in physical and biological complexity.
The part of thermodynamics known as biological thermodynamics describes
well the main phenomenological properties in energy transformation in the biological world. Because the hierarchy of the biological world is tremendous, statistical
concepts based on two-level physical models of macroÀmicro relations are not
effective in producing a description, as they are in statistical mechanics/
thermodynamics.
Can biological hierarchy be described in terms of entropy, in a fashion similar to a hierarchal description in thermodynamics—the two-leveled model of
hierarchy? If we are sure that the universal entropy definition can be defined,
then (1) it is a universal description for both physics and biology, (2) it can be
universal for different biological organizational levels (e.g., for cell and for society)—we might need to concentrate on this route. However, if we are not sure
that it is possible, we should not ignore the need to seek the development of
other approaches. Another possible approach is the pure phenomenological
approach based on the relationship between kinetics and energetical transformations. We, therefore, will concentrate on phenomenology, on the parameters that
are related directly to the energetical properties of processes. At this stage, we
see this way as being important to the development of a common interface for
physics and biology.

18

The Common Extremalities in Biology and Physics

Certainly, the models of hierarchy of physical phenomena are not limited to the
two-level classical physics model. Some examples can be shown by quantum statistics,
e.g., BoseÀEinstein or Fermi statistics—hierarchical concepts based on symmetries in
particle physics or atomÀnucleiÀquarksÀstrings. However, by comparing the hierarchy in the fields of physics/thermodynamics and biology, it is easy to see that we are
dealing with levels based on the laws of classical physics. Molecules and macromolecules in biology (biological thermodynamics and kinetics) are considered as classical
objects. So, by simply regarding the microlevel in thermodynamics, while comparing
the hierarchy with biology, we consider only classical thermodynamics/statistics-based
mechanics and physics. In this sense, classical thermodynamics can be thought of as
being a two-level hierarchical model. Certainly, this description should be balanced in
the sense of the micro- and macroparameters involved.

1.2
1.2.1

Extreme Properties of Energy Dissipation
Comparing Extreme Approaches

The extreme approaches can be said to represent the pinnacle of physics formalism.
Extreme approaches in physics are mathematically based on the variational techniques. Developed in recent decades, the unification and evolutionary physical theories are the best proof of it and paradoxically the variational extreme formalism is
not just the formalizational pinnacle and the perfect technical basis, but also penetrates deeply the nature of physical phenomena. However, thermodynamics still has
some difficulties in developing such a consistent variational formulation, as have
the branches of mechanics or physics of fields.
The classical expansion of the description in classical thermodynamics conceptually proceeds from the formulation of the laws of the equilibrium state and then
addresses the simplest nonequilibrium state—the stationary one. Later, classical

thermodynamics was lost in the different approaches to describe the increasing
variety/branches of nonequilibrium states. However, obviously, there is a necessity
for the common ideological and technical description of the infinite variety of nonstationary states and processes considerably removed from the equilibrium and
being stationary—e.g., the biological processes.
At the same time, it is obvious that nonstationary and nonequilibrium processes
and states occur in nature even more frequently than stationary ones and more so
equilibrium states. One can say that the matter moves because it is in nonequilibrium.
Therefore, one could try to alter the conceptual direction of the classical thermodynamic consideration and employ a methodological inversion, i.e., it is probable that
one needs to proceed in developing the thermodynamic description of the nonstationarity directly from the laws of inequilibrium and instationarity. In this moment, it
needs to give the answer to the question: Do unstable or nonstationary states have a
common law?
Furthermore, one can say that the main characteristics of all nonstationary and
nonequilibrium states are probably that they are striving to the equilibrium or