A General Thermodynamic Theory for Dynamic Order Existence

1
A General Thermodynamic Theory for Dynamic Order
Existence Evolution

• Prof. S. P. Mahulikar

• Introduction Review
• Negentropy re-defined
• Negentropy Principle (NEP)
• Principle of Maximum Negentropy Production
  (PMNEP)
• Conclusions

2
Introduction

• Entropy Principle implies reduction in magnitudes
  of gradients of field variables globally
• Reducing ?Grad(F)?g and increasing S are
  concurrent synonymous i.e. S???Grad(F)?g?
• Background Review
• Negentropy
• What an order feeds upon is negentropy
• E. Schroedinger, University Press, Cambridge,
  1945
• What is Life? The Physical Aspect of the
  Living Cell
• Negentropy is mobilisable stored energy in a
  self-organized system
• M-W. Ho, Modern Trends in BioThermoKinetics 3,
  50-61, 1994
• Directives for dynamic order creation existence
  were stated using reverse concept of entropy
• S.P. Mahulikar, H. Herwig, Physica Scripta, 70,
  212-221 (2004)

3
Background Review (contd.)

• Fractal-Based Scaling Universality of Order
• Biological evolution is part of universal process
  of evolution
• H. Spencer, Williams Norgate, London, 1862
  First Principles
• Ordered patterns are fractal-based exist at
  boundary between order disorder, evolve by
  increasing their complexity during development
• G. Damiani, P.D. Franca, Rivista di Biologia -
  Biology Forum 90, 227-266, 1997
• Universe essentially fractal-on scale of galaxies
  their clusters
• K.K.S. Wu, O. Lahav, M.J. Rees, Nature 397,
  225-230, 1999
• Universality discussed in evolutionary origin
• M.Y. Azbel?, Physica A 353, 625-636, 2005

4
Background Review (contd.)

• Order Evolution
• Evolution Definitions
• Process of transformation of less ordered to more
  ordered states, following from natural law
• H. Spencer, Williams Norgate, London, 1862
  First Principles
• Irreversible accumulation of effects of
  historical contingency
• S.N. Salthe, MIT Press, Cambridge MA, 1993
• Development Evolution Complexity Change
  in Biology
• Evolution Postulates
• Life on Earth arose from non-living matter
  proceeded to evolve into more complex forms, by
  random mutation natural selection process
  (popularly known as survival of fittest).
• C. Darwin, Murray, London, 1859
• On the Origin of Species by Means of Natural
  Selection
• Mutations alone can bring about abrupt
  noticeable evolutionary changes in dynamic order
  (Mutation Theory)
• H. de Vries, Die Mutationstheorie, Veit Comp.
  Leipzig, 1901, vol. 1.
• Versuche und Beobachtungen über die Entstehung
  von Arten im Pflanzenreich

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Background Review (contd.)

• Emergence of life from inanimate matter yields
  novel insights when discussed in light of
  thermodynamics
• A.C. Elitzur, J. Theoretical Biology 168,
  429-459, 1994
• Evolutionary entropy rather than Malthusian
  parameter represents non-equilibrium analogue of
  thermodynamic entropy
• L. Demetrius, Proc. Nat. Acad. Sci. USA 94,
  3491-3498, 1997
• Evolutionary potential proposed (incorporating
  entropy) necessary condition for ordering
• A. Corbet, Complexity 8, 45-67, 2003
• Evolution produces ever more ordered matter,
  while also increasing its complexity
• Y. Neeman, Found. Phys. Lett. 16, 389-394, 2003
• Stable evolution through natural selection is
  manifestation of non-equilibrium thermodynamic
  derivatives
• K. Michaelian, J. Theoretical Biology 237,
  323-335, 2005

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Inferences from Review

• No universally accepted definition of negentropy
  that enables explanation of order origin,
  existence, evolution.
• No guiding physical principle, identified to
  determine order evolution.
• Universality in evolutionary origin, selection,
  mortality.
• Creation, existence, evolution, destruction of
  order, in biology cosmology, are within the
  same fractal with patterns governed by
  thermodynamics.
• Thermodynamic principles enable dealing with
  arbitrary complex ordered systems from a
  universal point of view
• H. Hermann, Springer-Verlag, Berlin-Heidelberg,
  1988
• Information Self-Organisation
• Thermodynamic principles for order are valid for
  all scales.

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Objectives Scope

• Scope Analysis of qualitative macroscopic
  phenomena.
• Assumption i) Isolated system is embedding i.e.
  it can embed open systems, e.g. order
• Assumption ii) gt0
• Isolated System (IS) is sufficiently far from
  equilibrium for it to be unstable localised
  order in disorder is manifestation of this
  instability
• as isolated system approaches equilibrium,
  lt0

• Path taken by isolated system is governed by Law
  of Maximum Entropy Production (LMEP)
• which explains role of order in global entropy
  increase
• based on preference for path of least resistance
  for minimizing net magnitude of global gradients
  of field variables, ?Grad(F)?g

Illustration of regimes on entropy-time diagram
for Isolated System (IS)
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Objectives Scope (contd.)

• EP LMEP are fundamental Laws of Physics that
  determine spontaneity.
• Rate at which ?Grad(F)?g is diminished can be
  interpreted as degree of spontaneity.
• faster rate at which net global gradients of
  field variables are diminished, higher is degree
  of spontaneity
• quantitatively determined by rate of entropy
  change
• gt0 represents a spontaneous process
• Entropy Principle states that gt0 (in net)
• LMEP states that isolated system selects paths or
  their assemblages that maximise net degree of
  spontaneity ( is maximised).
• occurrence of non-spontaneous processes in nature
  justified as they result in net positive degree
  of spontaneity ( gt0)
• LMEP further implies that non-spontaneous order
  creation existence are paths that result in net
  higher degree of spontaneity than by spontaneous
  processes alone
• Creation existence of order are paths of lesser
  resistance relative to total disorder, for
  diminishing ?Grad(F)?g faster
• for given ?Grad(F)?g minimising resistance leads
  to maximising the rate/s of irreversible
  process/es J i.e. J??Grad(F)?g, is maximised
• ?2SIS is Lyapounov fn for large deviations from
  equilibrium I. Prigogine, Science 1978

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Objectives Scope (contd.)

• To right top (I-quadrant) of IP
• SIS increase gradually approaches asymptote.
• System characteristics are determined by its
  inertia which prevents system from reaching
  global equilibrium 0 ?Grad(F)?g0
• System settles down to tendency based on Theorem
  of Minimum Entropy Production (TMEP) I.
  Prigogine, 1961
• Stable static order can exist whose objective is
  to freeze localised entropy production
• Global entropy production rate reduced in this
  regime
• dynamic order is not supported by surroundings.
• dynamic order produces higher entropy ( faster
  rate of approach to equilibrium)
• For low disequilibrium, irreversibilities in
  disorder diminish low gradient/s of field
  variable/s
• net excess entropy cannot be generated by
  localised dynamic order
• inequality ( lt0) implies that disordered
  isolated system is stable
• creation existence of dynamic order satisfy
  inequality ( gt0), feasible to left of IP

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Objectives Scope (contd.)

• Assumption iii) Isolated system is dynamically
  unstable chaotic.
• This assumption is subset of Assumption ii)
• additional condition imposed by is large no. of
  interactions within IS
• Stable existence of unstable order in disorder
  necessitates stable exchange of mass / energy,
  stabilised as per Law of Large Numbers I.
  Prigogine, 1978

Negentropy Re-Defined

• Negentropy should encompass following
  perspectives
• Have negative sign, but its implication/s should
  extend beyond
• units either of entropy or specific entropy
• enable accounting for existence E. Schroedinger
  (1945) evolution
• Since S ? 0 A. Tamir, Canadian J. Chemical Engg.
  80, 1002, 2002 , negentropy is necessarily
  relative measure of deviation from equilibrium of
  ordered sub-system with respect to its
  surroundings

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Negentropy Re-Defined (contd.)

• Re-Definition of Negentropy (sni) of Ordered
  Sub-System (oi)
• sni soi?sd
• soi specific entropy of ith order, sd specific
  entropy of the surroundings (disorder).
• Negentropy is specific entropy deficit of order
  with respect to its surroundings
• soiltltsd ? snilt0
• sni reduces to zero when order oi completely
  merges with disorder
• sni is measure of contrast of ordered sub-system
  relative to surroundings
• SIS md?sd mIS md, sIS
  soi?sni
• Ne is no. of ordered sub-systems existing
• definition of sni leads to direct thermodynamic
  principles for order existence evolution,
  complementary to EP LMEP
• increase / decrease of sni discussed in these
  principles are its absolute value (?sni?)

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Negentropy Principle (NEP)

• Statement of NEP
• For dynamic order to exist (or when dynamic
  order exists), its negentropy must increase (?
  ?gt0 ? lt0)
• Conversely, when ordered sub-system oi ceases to
  exist, its negentropy begins to decrease (i.e. ?
  ?lt0 ? gt0), until sni0 (? soisd)
• sIS Eq. (4.1) increases, since SIS increases
  (as per Entropy Principle) and mIS is fixed
• (moi/mIS)?0 ?0
• mass of ordered sub-systems is much lower than
  mass of isolated system
• last term on the right hand side of Eq. (4.1) is
  negligible
• Increasing sIS (Eq. 4.1) implies two exclusive
  possibilities
• ?sni must increase (NEP ? ? ?gt0),
  dynamic order exists
• If ?sni reduces or remains the same, order oi is
  converted to disorder

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The Negentropy Principle (contd.)

• NEP can be proved directly by differentiating Eq.
  (3) with respect to time
• If dynamic order oi exists, specific entropy is
  maintained relative to surroundings
• practically,
• ,
• EP?NEP, when dynamic order exists.
• For dynamic order oi to co-exist with disorder,
• soi?soi,thr
• specific entropy of oi must be lower than
  threshold (else ? ?lt0 NEP is violated)
• ?Grad(F)?oi,thr is threshold magnitude of
  gradient of field variable across oi
• If Grad(F)?oigtGrad(F)?oi,thr, oi is destroyed,
  because soigtsoi,thr
• To satisfy Entropy Principle ?Grad(F)?g lt
  ?Grad(F)?g.

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The Negentropy Principle (contd.)

• Dynamic order is unstable open system Hermann,
  1988 maintained by stable influx of energy /
  or matter

• oi maintains its specific entropy soi (i.e.
  ?0) by interaction with its surroundings.
• interaction is in form of mass / energy exchange
  with surroundings
• Mass enters ordered sub-system at flow rate ,
  and associated entropy rate
• Energy ( ) can flow in at associated entropy
  rate

Thermodynamic representation of dynamic order
existence
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The Negentropy Principle (contd.)

• Variations in soi are much smaller relative to
  increase in sd
• Variations in moi Eoi are much smaller relative
  to .
• gtgt , gtgt
• Ordered sub-system oi maintains gradients of
  field variables across its boundary
• ?Grad(F)?oi ? ?Grad(F)?oi,thr
• Mass / energy exchange increases values of
  gradients of field variables that can be
  maintained increases
• Increased ?Grad(F)?oi,thr is due to increased sni
• necessitates higher rate of entropy production
• sni??? ??
• Total Entropy generation is
• entropy generation due to
  irreversibilities not related to order oi

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The Negentropy Principle (contd.)

• If oi is replaced by its surroundings (disorder)
• same mass (moi)
• higher specific entropy sd( ) gtgt soi,
• then gt , gt
• ltlt , ltlt
• During comparison
• are kept same as reference values
  
• For isolated system in state of total disorder
• negentropy debt Compensation by first two terms
• Order produces entropy at rate sufficient to
  compensate for internal ordering
• balance equation based on Entropy Principle is
  not violated (Schroedinger 1945)

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The Negentropy Principle (contd.)

• Total entropy generation rate in isolated system
  at t is
• is due to existence of Ne
  ordered sub-systems
• is due to creation of Nc ordered
  sub-systems
• is to destruction of ND ordered
  sub-systems
• Order evolution is included in the existence
  term
• Probabilistically created high ?Grad(F)?oi
  gtgt?Grad(F)?oi,thr
• destroy dynamic order
• Event of destruction of unstable order is
  bifurcation point
• negentropy vanishes
• Extinction of particular species is due to
  inability to avoid high ?Grad(F)?oi

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Principle of Maximum Negentropy Production (PMNEP)

• Statement Isolated system comprising of order
  co-existing in disorder will select path or
  assemblage of paths out of available paths that
  maximizes negentropy of order at fastest rate for
  given constraints
• ? ?is highest for given constraints
• Two possible ways to realise LMEP when order
  exists
• ?sni must increase at fastest rate for given
  constraints
• If ?sni reduces or remains same, oi is destroyed
  into disorder.
• Evolution to superior forms combines two
  features
• Ability to avoid ?Grad(F)?oi that exceed
  Grad(F)?oi,thr
• Ability to generate negentropy at increasing rates

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Review on evolution, role of PMNEP as Law of
Evolution
20
Review on evolution, role of PMNEP as Law of
Evolution (contd.)
21
Review on evolution, role of PMNEP as Law of
Evolution (contd.)
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Explanation for Coexistence of Superior
Inferior Order

• Entropy generation due to order existence given
  by
• Evolution leads to order with higher sn ,
  i.e. superior
• all ordered sub-systems are not converted to
  superior
• Combination of superior inferior max.
• referred as enslaved modes (Hermann 1988)
• Ordered sub-systems that generate higher sn (
  ) tend to enslave those that generate lower sn (
  )

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Conclusions

• Negentropy is specific entropy deficit of order
  w.r.t. surroundings
• PMNEP encompasses ideas behind evolution
  postulates by Darwin de Vries.
• Evolution is selection of different path/s or
  their assemblages
• Whenever ordered sub-systems exist, they evolve
• Validity of NEP implies validity of PMNEP, vice
  versa also holds.
• Superior forms have high negentropy, which
  implies is implied by high negentropy
  production rate
• Co-existence generates more entropy
• Explains increased evolutionary entropy with
  evolution.
• Paths for maximising global entropy production
  rate under given constraints Creation,
  existence, evolution, destruction of order

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Unification of dynamic order creation, existence,
evolution, destruction, solely by thermodynamic
principles