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The phase space interpretation of the Le Chatelier‐Braun principle and its generalization as a principle of natural philosophy

Authors:
  • Orta Dogu Teknik Universitesi (Middle East Technical University), Ankara, Turkey

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.
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 ¼krTðheat flow;Fourier’s lawÞ;(4)
JC¼dm=dt ¼DrCðmass flow;Fick’s lawÞ;(5)
Je¼dQ=dt ¼KrUðelectric current;Ohm’s lawÞ;(6)
Jch ¼dN=dt ¼r
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.
826
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.
2932
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 ÞSðT!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
e¼N@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:
rE¼@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.
4446
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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