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The phase space interpretation of the Le Chatelier–Braun principle

and its generalization as a principle of natural philosophy

O

¨zdog˘an Gu¨ndu¨z

1

and Gu¨ngo¨r Gu¨ndu¨z

2,a)

1

Gu¨ zelyalı Mah., 331.So. 9/2, Go¨lbası, Ankara 06830, Turkey

2

Kimya Mu¨ hendislig˘i Bo¨lu¨mu¨ , Orta Dog˘ u Teknik U

¨niversitesi, Ankara 06800, Turkey

(Received 10 September 2013; accepted 16 July 2014; published online 12 August 2014)

Abstract: The well-known Le Chatelier principle in chemistry describes how a system behaves

when subject to an external effect. The way this principle works in conservative and dissipative

systems was discussed within the framework of phase space. The Le Chatelier principle was

restated in a more generalized form in such a way that it now becomes an underlying principle of

many natural phenomena. The Lenz law in electromagnetism and deformations of materials

were treated within this context. The increase of entropy and the adaptability of biological

organisms in evolution were also discussed from the standpoint point of view of the generalized

principle. V

C2014 Physics Essays Publication.[http://dx.doi.org/10.4006/0836-1398-27.3.404]

Re´ sume´: En chimie, le principe bien connu de Le Chatelier de´ crit la fac¸on dont un syste`me se

comporte lorsqu’il est soumis a` un effet externe. La manie`re dont ce principe fonctionne dans les

syste`mes conservatifs et dissipatifs a e´te´ discute´e dans le cadre de l’espace des phases. Le principe

de Le Chatelier a e´te´ reformule´ dans une forme plus ge´ne´ ralise´ e de manie`re a` devenir un principe

sous-jacent a` de nombreux phe´nome`nes naturels. La loi de Lenz en e´lectromagne´tisme et les de´ for-

mations de mate´riaux ont e´te´ traite´es dans ce contexte. L’augmentation de l’entropie et l’adaptabi-

lite´ des organismes biologiques dans l’e´volution ont aussi e´te´ discute´es du point de vue du principe

ge´ne´ralise´.

Key words: Le Chatelier–Braun; Chemical Equilibrium; Lenz Law; Entropy; Deformation; Adaptability; Evolution.

I. INTRODUCTION

The Le Chatelier principle describes the behavior of a

chemical system at equilibrium subject to an external force.

It brieﬂy says:

(i) “If any of the variables such as pressure, volume, tem-

perature, and concentration under which a chemical

system sustains its stability is forced to change, the

system shifts its equilibrium to a new state to counter-

act the imposed change.”

It is sometimes stated in more general terms as:

(ii) “Any change in current situation generates an oppos-

ing reaction in the system.”

A better deﬁnition is:

(iii) “An external interaction which disturbs the equilib-

rium brings about processes in the body which tend to

reduce the effects of this interaction.”

1

The explanation of this principle is usually done using a

reversible gas phase chemical reaction system.

AþB!

C:(1)

The two-way arrows designate the reversibility of the sys-

tem. Let us assume this reaction to be at equilibrium. If some

more A or B is added the reaction shifts to the right and pro-

duces more C, such that the equilibrium is re-established.

The newly addition of A or B actually increases not only the

concentration but also the pressure, so the system moves in

the direction to reduce it. If an external pressure is applied

on the system without introducing new A or B the system

again behaves in the same way, shifts to the right, and pro-

duces more C to relieve the external pressure applied. If heat

is supplied to the system the shift occurs in a direction to

absorb the given heat. If A þB!C direction is exothermic,

some C decomposes to give C !AþB such that the given

heat is absorbed for the decomposition of C, or if the reaction

is endothermic, heat is absorbed to produce more C.

The principle underlying these chemical changes can be

extended to other natural phenomena of all kinds no matter

whether it is in physical world or in human relations,

economics etc.

The principle was introduced by Le Chatelier in 1884 as

a qualitative statement, and Braun established a scientiﬁc

framework in 1887–1888; and it is also known as the Le

Chatelier–Braun principle.

II. ENERGY AND FLUX

All changes in chemical equilibrium systems can be

interpreted by using the Gibbs–Duhem equation that can be

easily derived from the Gibbs free energy equation and the

Maxwell relations. Its derivation can be found in physical

chemistry and thermodynamics textbooks. It is given as

dG ¼VdP SdT þX

i

lidni;(2)

a)

ggunduz@metu.edu

0836-1398/2014/27(3)/404/7/$25.00 V

C2014 Physics Essays Publication404

PHYSICS ESSAYS 27, 3 (2014)

where G is free energy, V, P, S, and T are volume, pressure,

entropy, and temperature, respectively. The last term is due

to chemical change, and l

i

and n

i

denote the chemical poten-

tial and the number of molecules of the ith species, respec-

tively. The change in any of the terms of Eq. (2) changes the

others as expected to keep dG ¼0. This equation involves

the mutual effects of all moments, i.e., (i) zeroth moment,

mv

0

(or n), (ii) ﬁrst moment, mv

1

(or P), and (iii) second

moment, 1

=

2mv

2

(or T).

Chemical equilibrium is a very dynamic system. The

experiments showed that an inﬁnitesimal addition of a radio-

active isotope of reactant (A or B) which is so small that it

cannot disturb equilibrium, in fact, caused the formation of a

radioactive product (e.g., radioactive C molecules). The

chemical equilibrium constant K for Eq. (1) is simply given

by

K¼½Ceq

½Aeq½Beq

;(3)

where the brackets designate the equilibrium concentrations.

At the equilibrium, K ¼1; and according to the Le Chatelier

principle an increase in the value of concentration either in

numerator or denominator changes to keep K ¼1. It is usu-

ally difﬁcult to understand what really happens dynamically;

and the change in mass balance is interpreted in a trivial way

as “if concentration is changed in one side, the concentration

in the other side also changes to keep the system at equi-

librium.” The change in pressure or temperature affects the

concentrations but they are related to each other by some

other relations such as ideal gas law.

Besides the chemical change, all other equations involv-

ing ﬂow have the same mathematical form such, as

Jq¼dq=dt ¼krTðheat flow;Fourier’s lawÞ;(4)

JC¼dm=dt ¼DrCðmass flow;Fick’s lawÞ;(5)

Je¼dQ=dt ¼KrUðelectric current;Ohm’s lawÞ;(6)

Jch ¼dN=dt ¼r

nGðchemical changeÞ:(7)

These equations can be put into a general form so-called the

Onsager relation,

J¼LX;(8)

where X is the gradient of the driving force or afﬁnity and J

is ﬂux or reaction rate; L is a coefﬁcient not depending on ei-

ther X or J. X creates J according to Eq. (8), which actually

represents “cause-effect” relation. Equations (4)–(7) were

derived from experimental facts, therefore the constants L

are known as phenomenological coefﬁcients. When there are

numerous processes occurring simultaneously, Eq. (8) can be

generalized as

Ji¼X

j

LijXj:(9)

The entropy change in time (dS/dt) can be expressed also in

terms of X and J, such that

dS

dt ¼r¼X

j

XjJj;(10)

where the summation is done over all extensive variables

such as energy or volume; and ris called dissipation

function. The combination of Eqs. (8) and (10) gives

r¼X

i;j

LijXiXj:(11)

As the thermodynamic forces X

i

are arbitrary, and r>0 for

a nonequilibrium system the diagonal kinetic coefﬁcients are

always positive, that is,

Lii >0:(12)

If a stationary state is slightly disturbed, it returns to its ini-

tial state after a while. Let us assume that the system which

is under the balance of forces X1;X2; ::::Xkis disturbed by a

small external force dXi;ði>kÞ. The ﬂux given by Eq. (9)

which is zero in the stationary state becomes dJi¼LiidXiin

the perturbed state as can be easily deduced from Eq. (9).

Then, Eq. (11) gives

dJidXi¼LiiðdXiÞ2>0:(13)

According to this relation, an increase in dXiincreases the

ﬂux dJi. However, the increase in ﬂux always decreases the

force which causes it. This is nothing but the Le Chatelier

principle; the increase in dJidecreases dXiand restores the

stationary or equilibrium state.

The entropy of a steady-state system exchanging mass

and heat with the surrounding medium can be simply written

as follows by using Eq. (11):

r¼JHXHþJMXM;(14)

where the subscripts H and M denote heat and mass, respec-

tively, and

JH¼L11XH;JM¼L22 XM:(15)

Consider a stationary state with the conditions of

JM¼0;XM¼X0

M;JH¼J0

H;XH¼X0

H:

The deviation from this state may be possible due to a small

variation of the force X

M

by dX

M

, such that

dJM¼L22dXM:(16)

Then the entropy production r

0

before the perturbation

changes by a small additional term,

r¼r0þL22ðdXMÞ2:(17)

The r

0

is the minimum entropy production term and the

deviation from it will be positive,

dr ¼L22ðdXMÞ2>0:(18)

Since ðdXMÞ2>0, it is clear that L22 >0 in conformity with

Eq. (12).

2

The insertion of Eq. (16) into Eq. (18) yields

Physics Essays 27, 3 (2014) 405

dr ¼dJMdXM>0:(19)

This inequality designates the Le Chatelier–Braun principle.

3

The variation of the force (i.e., dXM) gives rise to a variation

in current (i.e., dJM) of the same sign. It means the variation

in current reduces the effect of variation in force.

The traditional interpretation of the Le Chatelier princi-

ple is somehow restricted although some interesting applica-

tions are found in economics and in biology. The economist

Samuelson introduced Le Chatelier’s principle into economy

in 1947 to explain the price equilibrium.

4,5

The Le Chatelier

principle ﬁnds many applications in a diverse variety of

ﬁelds, even in cosmological physics.

6

It is also applied in

biology to explain homeostasis which is deﬁned as the prop-

erty of a system to regulate its internal parameters to coun-

teract environmental changes to maintain its stability. The

living organisms have to show adaptation to the changing

conditions to survive. In fact, only those species which ex-

hibit adaptability can survive and give offsprings, which,

then look for future stability. In fact only those species which

have stability at varying conditions can have a chance to

multiply. It is worth to note that this stability needs to be

dynamic stability to cope with the multiparameter conditions

of environment.

However, there had also been severe criticisms of this

principle in the past led by De Heer based on the statements

of Ehrenfest and Raveau about the ambiguity of the principle

as quoted in his work.

7

De Heer suggests “to replace the Le

Chatelier–Braun principle by a small number of rules each

of which has a limited range of applicability and is less am-

bitious (such as the ones given by van’t Hoff).” There have

been numerous studies to deﬁne it in a more explanatory

way and to understand its meaning, and to explain the condi-

tions of its applicability.

8–26

De Heer strictly concentrated on

the state of chemical equilibrium and claimed that the system

did not have to oppose or relieve the applied perturbation,

and he supported his argument by some examples from phys-

ical chemistry.

An external effect forces the system to change in certain

directions; however, the system develops a negative feed-

back to this change in accordance with the Newton’s third

law. The new equilibrium state can be far away from the for-

mer one, and it may take a long time to arrive at it. The fun-

damental action–reaction principle of Newton can also be

explained by the Le Chatelier principle, and its importance

should not be undervalued. Rather than “replacing the Le

Chatelier–Braun principle by a small number of rules”itis

much more meaningful to re-express it in a larger conceptual

context to cover much broader phenomena in nature. The

Ehrenfest’s question on differentiation of thermodynamic

properties of nonequilibrium states from those of equilibrium

states has been answered to some degree by Prigogine.

3

Actually nonequilibrium thermodynamics shifts the para-

digm from equilibrium states to processes. Processes should

be considered as autonomous entities and they cannot be

deﬁned as the changes in the state of objects.

27

The concepts

of nonequilibrium thermodynamics dispute the De Heer’s

arguments to weaken the importance of Le Chatelier princi-

ple, and instead trigger its use in more general sense.

In fact there is no perfect equilibrium in nature as stated

by the “continuous creation–destruction (corruption)” princi-

ple of Aristotle;

28

and all states are transient as also stated by

chaos theories.

29–32

Molecular and biological evolutions also

occur according to this natural principle.

The chemical equilibrium as a dynamic process can be

deﬁned as a state where forward and backward rates

(i:e:; r!and r ) are equal, i.e.,

r!¼r or r!r ¼0:(20)

In this form, it looks like a ﬂow equation, and the Gibbs–

Duhem equation (i.e., Eq. (2)) then can be written as

follows:

G!G ¼ðP!P ÞSðT!T Þ

þX

i;j

ðlin!ljn Þ:(21)

The change in A þB!

C due to change in concentration,

temperature, or pressure is actually a distortion in the phase

space of the system. That is, the kinematic and the potential

energy states of molecules change if the system is distorted.

In other words, positions, velocities, and also vibration, rota-

tion, and electronic conﬁgurations of molecules change to

attain new equilibrium. The system moves out from a previ-

ous equilibrium state to a new equilibrium state via the gen-

eration of material and energy ﬂuxes; and it can reach

stability only if the external causes are counteracted by

absorbing the external energy input in the form of kinematic

and potential energies at molecular level. Such systems are

known as dissipative systems,

33

and energy dissipation goes

extinct if ﬂuxes (or currents) of material and energy stop

feeding the system. The system then ﬁnally arrives at its new

equilibrium state. Dissipative systems have a kind of order in

their structure, and can sustain it only at the expense of

increasing the entropy of a “larger system” in which the dis-

sipative system is embedded. The change from an equilib-

rium state to a dissipative state or to another equilibrium

state takes place only through ﬂuxes. As the great philoso-

pher Heraclitus said in the Ancient times, “everything occurs

through ﬂuxes.”

34,35

The creation of ﬂuxes naturally involves

entropy production or irreversibility, because, ﬂuxes distort

the surrounding environment. In other words, the persistent

change in nature can be achieved only by increasing the irre-

versibility. The change from one equilibrium state to another

one can be accomplished only through the creation of gra-

dients which are the driving forces that generate the ﬂuxes.

In this respect, the initial and the ﬁnal equilibrium states

behave like attractors connected by ﬂuxes; or like opposite

electric charges connected by electric ﬁeld lines, or magnetic

poles connected by magnetic ﬂux.

III. COUNTERACTION IN PHASE SPACE

The physical laws can be categorized in two groups, (i)

those which are nonmathematical and do not involve the

concepts of space and time, and (ii) and those stated by

mathematical relations between the properties of matter,

space and time.

36

Although the Le Chatelier–Braun principle

406 Physics Essays 27, 3 (2014)

is stated in a nonmathematical form, it involves space and

time in its applications. There is no space and time concept

in chemical equilibrium, but they are involved when equilib-

rium is perturbed.

According to the very fundamental principles of classi-

cal physics, the motion of an object occurs in the direction of

applied force, i.e., an applied force induces a movement (or

ﬂux) in its own direction. The term “current” is used instead

of “ﬂux” in the physical equations such as the Fourier’s heat

conduction law, the Fick’s law, and the Ohm’s law; all of

which have the same mathematical structure. This Newto-

nian approach to describe action–reaction phenomenon in

nature purely depends on interactions of rigid bodies which

do not deform on collisions where causality principle works

perfectly. It is well-known that in quantum mechanics cau-

sality principle fails because interactions are not rigid body

interactions, and an object subject to an external force is no

more the one before interaction, because, the previous wave

function collapses after the interaction and the system is then

described by a new wave function. No matter whether we

describe chemical reactions in terms of classical or quantum

mechanics the molecules are always subject to deform per-

manently after the reaction, i.e., they change into another

persistent shape, or into a state described persistently by a

new wave function.

In phase space, molecules are described by their posi-

tions and velocities, and only the changes in positions and

velocities of molecules are of concern for dynamical descrip-

tion. The chemical reactions or phase transitions both change

the phase space. Since the deﬁnition of phase space is based

only on position and velocity the ﬂux (or current) due to

deformational change as in chemical reaction (i.e., change of

shapes of molecules) cannot be explicitly expressed simulta-

neously with dynamical changes within the context of con-

served phase space. In fact, the perturbation of phase space

by any cause yields a change in entropy which is a measure

of deformation or of degradation.

Whether phase space is conserved or not the question is

in what way it reacts against an external force; in other

words, how reaction reveals within the context of action–

reaction principle. Since phase space (C) has two compo-

nents as space (position) and momentum (velocity) the

change in one of them inﬂuences the other. The change in

phase space (dC) can be simply given in terms of the change

in space (ds) and the change in momentum (dp), such that

37

dC¼ds dp:(22)

In a conservative system, phase space is conserved and the

change in the magnitude of one of the components inversely

affects the other to keep dCconstant. In dissipative systems

dCis not conserved but the inverse dependence is still valid

though it is not one to one. In conservative systems one of

the components of dCacts as the potentiality of the other in

the Aristotelian sense.

38

That is, if ds contracts dp expands

or vice versa. For instance, in a “cylinder-and-piston” system

the contraction of space (e.g., volume, V, or ds) is due to the

increase in pressure P (or momentum, dp). This is actually

the well-known Boyle–Mariotte law (i.e., PV ¼constant).

The physical deformation (contraction or expansion, or

decrease or increase) in either one is reversible in conserva-

tive systems. In the case if temperature also changes, we

may have dissipative system, but still ds and dp behave in a

similar manner. If one of the variables is changed the system

reorganizes itself by readjusting the variables of the phase

space. The adjustment can ﬁnally yield reversible or irrevers-

ible state depending whether the phase space is maintained

or is degraded.

In dissipative and chemically reacting systems, dCis not

conserved and a ﬂux is created at the expense of the irrevers-

ible decomposition of dC. The reversible deformation of ds

and dp (i.e., the change of the magnitudes of ds and dp) in

conservative systems signiﬁes a reversible transient state,

and it becomes irreversible only if dCdecomposes to a new

value, say dC0. Every new input can change the phase space

into new forms, i.e., dC!dC0!dC00 !dC000:::.

Any parameter which can sustain itself against the long-

term reactive changes (or permanent changes) in the course

of evolution can be carried into future. This is what is known

as adaptability in biological evolution. Adaptability is

actually the persistence of some of the appropriate parame-

ters of the system but allowing relatively small changes in

some other parameters. What is apt to change or to evolve is

what cannot resist the forces affecting because of being at a

lower stability state. What perishes and what comes in new

both provide the new potentiality for the adaptability of the

nonperishing parameters of the system.

The dissipative process increases entropy and reveals

persistency or irreversibility of a new state which is sup-

posed to be more stable than the former state under new con-

ditions. In other words, the newly evolved system can be

persistent only if the former phase space is degraded and

rebuilt. However the new state is also transient in the long

run and forced to change by oncoming processes. All these

reveal through the partial changes caused by the generation

of ﬂuxes. In this sense, whether the system is conservative or

dissipative the system always tries to adjust itself against the

external effects. So the Le Chatelier principle can be modi-

ﬁed and generalized to the following form:

“If any of the variables under which a system sustains its

stability is forced to change, the system adjusts itself to the

new conditions by changing its equilibrium to a new state

which ﬁts to the changed (new) conditions.”

The reason why ds and dp act in an inverse manner has

roots in the very basic deﬁnition of velocity; the instantane-

ous velocity is always tangential to trajectory as it denotes

the slope. In fact phase space is nothing but a simple tangent

space. An opposing or relieving type of reaction revealed

according to the Le Chatelier–Braun principle takes place

through the changes taking place in the tangent space. Any

effect produced in the coordinate space due to an external

cause can also induce another effect in the velocity space, or

vice versa.

IV. THE LENZ LAW

The tangent space (or phase space) interpretation of Le

Chatelier principle can be best understood by considering the

Physics Essays 27, 3 (2014) 407

law of induction in electromagnetism. According to the Lenz

law,

“An induced current is always in a direction to oppose

the motion that causes it.”

This deﬁnition is in perfect agreement with the deﬁnition

of the Le Chatelier principle given in “(ii)” in the introduc-

tion part. In more speciﬁc terms it can be restated as

“An induced electromotive force generates a current

whose magnetic ﬁeld opposes the original magnetic ﬂux.”

An induced electromotive force (e) and the change in

magnetic ﬂux (UB) are related to each other by

e¼N@UB

@t;(23)

where N is the number of loops in a coil.

The Faraday equation given by the following equation

describes how electric and magnetic ﬁelds induce each

other:

rE¼@B

@t:(24)

The induced magnetic ﬁeld inside any loop behaves in a way

to keep the magnetic ﬂux in the loop constant. The minus

sign indicates the direction of electromotive force. If the

magnetic ﬁeld is increased, the induced ﬁeld acts in opposi-

tion and decreases it; and if the magnetic ﬁeld is decreased,

the induced ﬁeld acts in the direction of the applied ﬁeld to

increase the magnetic ﬂux to keep it constant.

Here, electrical and magnetic ﬁelds act as if they are two

components of a phase space perpendicular to each other, the

positional change (i.e., r) concerns the change in electrical

ﬁeld whereas the change involving the rate (i.e., @=@t) con-

cerns the change in magnetic ﬂux. The change in one of the

components induces an effect in the other (i.e., vertical)

component to counteract the imposed change. This is so,

because electromagnetic ﬁeld is a vector ﬁeld, and the two

components (E and B) are perpendicular to each other. The

Le Chatelier principle works perfectly here, and the Lenz

law is its excellent application in electromagnetism.

The Lenz law can be used to understand how Newton’s

third law can be interpreted in electromagnetism. However

neither the third law nor the Lenz’s law explicitly explains

the mechanism of “deformational type of reaction” of a sys-

tem in terms of changes in tangent space (or phase space)

even though the Faraday equation is clearly deﬁned in this

space. In Newton’s third law, acting and reacting objects are

involved in rigid collisions and nothing is said about the ver-

tical direction as the material objects remain undeformed.

The Lenz law considers changes in both components of tan-

gent space; but the system is implicitly conservative. How-

ever, this is not the case in the deformation of material

objects.

V. DEFORMATION IN MATERIALS

Now, we can consider the most general case where the

system does not inherently possess two vertical components

as in electromagnetic ﬁelds, and in addition, the change (or

deformation) may be dissipative. There are two fundamental

laws which describe the dynamical behavior of material

objects at two extreme states. These are the Hooke’s law for

rigid systems and the Newton’s law for viscous ﬂow. The

Hooke’s law ﬁnds applications in material science describing

conservative so-called linear elastic deformations. Viscous

deformation is an irreversible process and not well recover-

able. The materials which exhibit partial recovery are said to

exhibit “plastic deformation.” The “elastic deformation”

such as tension or compression of a metallic, ceramic, or

polymeric specimen is given by

r¼EYe;(25)

where “E

Y

” denotes the Young’s modulus. This equation is

of the same form with the Hooke’s law, and the stress “r”

denotes the force applied per unit cross sectional area. The

fractional change in length “e” corresponds to the displace-

ment and “E

Y

” corresponds to the spring constant in the

Hooke’s law. In tension or compression the deformation

occurring along the axis also causes deformation in the verti-

cal direction. All these deformations go extinct upon the re-

moval of the stress applied. The system undergoes

deformation along axial and vertical directions to oppose the

externally applied stress. In case if shear stress is applied

(i.e., stress applied parallel to the cross section), the shear

stress “s” causes a deformation “c” expressed by

s¼Gc;(26)

where the constant “G” is called the shear modulus. Both the

moduli E

Y

and G can be expressed in terms of complex vari-

ables,

39,40

such that

EY¼E0

YþiE00

Y(27)

G¼G0þiG00:(28)

The real and complex components correspond to elastic and

dissipative terms, respectively. By the same token the modulus

G0and G00 are called “storage”and“loss” modulus, respec-

tively. In fact the stress “s” can be split into two components,

s¼s0þis00;(29)

where s0and s00 are stress components applied along the par-

allel (i.e., in-phase) and the vertical (i.e., out-of-phase) direc-

tions to the cross section of the specimen. If a specimen is

subject to a cyclic deformation given by

c¼c0sin xt;(30)

the elastic energy W

s

(or stored energy) and the dissipative

energy W

d

(or loss energy) can be given by

40

Ws¼1

2G0c2

0(31)

Wd¼p

4G00c2

0:(32)

These energy expressions are similar to the ﬁeld energies of

electrostatic (W

e

) and magnetic (W

m

) ﬁelds, such that

408 Physics Essays 27, 3 (2014)

We¼1

2eE2;(33)

Wm¼1

2lH2;(34)

where E and H represent the electrical, and the magnetic

ﬁelds, and eand lrepresent the permittivity, and the perme-

ability constants, respectively.

41

In electromagnetic ﬁelds, E

and H propagate perpendicular to each other similar to the

components of s(i.e., s0and s00). In both the electromagnetic

ﬁeld and the material stress ﬁeld the parallel and vertical

components store energy by the same natural phenomena so

that the mathematical expressions are of the same structure

as seen from Eqs. (31) and (32) to Eqs. (33) and (34). How-

ever, the second components (i.e., Eqs. (32) and (34)) differ

in their physical behavior; the magnetic and the electrical

ﬁelds are bound to each other and they copropagate in space,

one induces the other according to the Faraday’s induction

law. In material science, the Hooke’s law for rigid systems

and the Newton’s law for viscous ﬂow do not induce each

other when an external force acted on a viscoelastic material.

This is the point where the entropy is substantiated in sys-

tems where there is not a one-to-one dependence (or correla-

tion) between the components of the system, or when the

phase space cannot maintain its stability due to weakening of

correlations between its components. The degradation of

phase space brings in an increase of entropy and thus a

change in the information content which actually originates

from the change of the conﬁgurations of the molecules, or

the extents of correlations within the system.

42

Actually

there exists an analogy between electromagnetism and

hydrodynamics, and the behavior of electromagnetic and

hydrodynamic systems may resemble each other in some

cases.

43

The degraded new system can survive only if it is adapt-

able to new conditions, or if it is not reacted by whatever sur-

rounds it. At molecular level, a new molecule bounced into a

new surrounding medium can survive only if it maintains its

stability. For instance, an oxygen molecule given off in a

chemical reaction can survive at atmospheric conditions, but

a hydroperoxide molecule easily reacts with other molecules

in the environment or degraded by solar radiation and thus it

cannot survive for sufﬁciently long time. In biological world,

the process is same; any newly born organism is said to be

adaptable to the existing environment and multiply itself if it

can maintain its stability for sufﬁciently long time which is

the maturation time at minimum. So the stability of either

chemical molecules or biological organisms leads to adapta-

bility in the long run.

44–46

The continuous change of entropy

and the new information gained in time by complex systems

cause reorganization in molecular conﬁgurations. In other

words, the time dependent Kolmogorov–Sinai entropy and

the associated information content of an evolving system de-

velop in time in the resultant direction of the forces acting on

the system. These forces are always counteracted by the sys-

tem according to the generalized Le Chatelier–Braun princi-

ple, and the ﬁnal form of the system maintains its structure

and stays stable; or it survives if it is a biological organism.

The adaptability concerns with how evolution develops from

the actions and reactions of forces according to the general-

ized Le Chatelier–Braun principle.

VI. CONCLUSION

The Le Chatelier–Braun principle applied to chemically

reacting systems can be generalized to all other natural phe-

nomena. Its interpretation in tangent or phase space brings in

a uniﬁed view of the behavior of electromagnetic ﬁelds and

deformation dynamics of materials. The generalized concept

also helps to analyze the importance of entropy and adapta-

bility in evolutionary systems.

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