Conceptual Investigation of Entropy Principle: Identification of Directives for Creation, Existence

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Conceptual Investigation of Entropy Principle
Identification of Directives for Creation,
Existence Total Destruction of Order
Ref. Mahulikar, S.P., Herwig, H., 2004 (Oct),
Conceptual investigation of the entropy
principle for identification of directives for
creation, existence and total destruction of
order, Physica Scripta, Vol. 70, No. 4, pp.
212-221.
Keywords autocatakinetic, chaos, coherence,
cosmology, creation, destruction, entropy,
evolution, existence, irreversibility,
non-equilibrium, non-linearity, self-organising,
spontaneous order, stability, sustainability
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Background Motivation

• Origin of Observed Order Attributed to Unknown
  External Intervention
• change from disorder to order appears in
  violation of Entropy Principle
• Planck, M. attributed prevailing order in
  nature to purposeful activity
• (May 1937) Address, quoted in A. Barth, The
  Creation
• Einstein, A. - order is miracle that is
  strengthened by development of knowledge
• (1956) Letters to Maurice Solovine
• Major Revolution in Later Half of Previous
  Century
• spontaneous production of order from disorder is
  expected consequence of basic laws
  (Schroedinger-Bertalanffy-Prigogine)
• whether Chaos may produce sustain ordered
  structures patterns on large scale ?
• there is still considerable refinement
  necessary to understand fully how this works

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Objectives Scope

• Articulation of Thermodynamic Concepts
• irreversibility, entropy / generation, order
  disorder
• Enunciation of 9 Directives
• creation, existence total destruction of order
• illustration of directives thru conceptual
  model
• sustainability criterion stable order
  existence
• Isolated System
• large enough for all probabilistic events to
  occur
• large observation time interval
• interactions ? within isolated system
• system is far from equilibrium
• dynamically unstable
• chaos prevails

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Irreversibility Entropy

• Entropy Principle Implications
• systems spontaneously tend to go from less
  probable state in which they are relatively
  orderly organised (low entropy), to one that is
  more probable in which they are disorderly
  organised (high entropy)
• non-spontaneous change from disorder to order
  needs external intervention, which is
  irreversible loss
• Irreversibility
• characteristic of all non-linear systems
• superposition is invalid
• system cannot return back to its original state
  on its own by simply reversing output input
• irreversible loss
• inability to reverse to previous state without
  external intervention
• external intervention
• propagating loss over several non-linear systems
  in universe

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Concept of Irreversibility

• No Irreversible Loss if Reversibility is not
  Attempted
• allowing spontaneous flow of processes in nature
• irreversible loss realised when order exists
  with disorder
• need to return to original state or another
  specific (non-spontaneous) state for reducing
  entropy of order (for stable existence of order)
• continuous cost paid to reverse back to original
  state through real life irreversible processes
  thru non-linear systems
• Irreversibility - Relative Loss
• loss for order is gain for surrounding disorder
• entropy generation gain for disorder
• dispersion of gain in disorder (distribution of
  finite to infinite)
• disorder ?
• e.g Qin Wout Qrej Non-Linear System
  (Irreversible Process)
• Q (disordered form of energy) W (ordered form
  of energy)

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Entropy Principle

• Basic Realisations
• energy alone is not motive force for change
• energy possesses quality (w.r.t. order) in
  addition to quantity
• Entropy Clausius (1854) Annalen der Physik
• diminished gradients of field variables in
  dissipation process
• classical signpost of natural change
• S k?lnW Boltzmann (1886) The 2nd Law
• W no. - configurations a system can exist /
  no. - accessible states
• spontaneous change ? increase in accessible no.
  of micro-states
• macroscopic uniformity microscopic disorder
• Interpretation
• globally denies spontaneous emergence of ordered
  structure/s
• world goes from order to disorder
• falsified by spontaneous production of order
  from disorder
• spontaneous production of order from disorder
  infinitely improbable
• popular belief
• production of order required some outside agency
  or extra-physical operators

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Prelude to Order in Disorder

• Entropy Principle
• does not imply that ordered structures cannot
  ever emerge (locally)
• does not explain how ordered systems have arisen
  from disorder, maintained themselves in
  increasing disorder
• does not answer
• which out of available paths system will take to
  accomplish disorder ? ?
• Law of Maximum Entropy Production
• system will select path or assemblage of paths
  out of available paths that minimises potential
  or maximizes entropy at fastest rate given
  constraints Swenson (2000) Annals N.Y. Academy
  Sciences
• Order vs. Disorder An Examination of Contrast
• predictability of statistical system
• disorder (entropy) ?
• dispersion reduction of predictabilty
• order
• low tendency towards dispersion relative to
  surrounding disorder
• consistent coalescence concentration, for
  localised dispersion control

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Order vs. Disorder

• System Non-Linearity
• perfectly ordered system (all sub-systems
  linear)
• all resulting processes - reversible (linear in
  forward reverse directions)
• highly disordered system (more sub-systems -
  highly non-linear)
• Identity of Ordered Sub-System
• order - neat, patterned with identity (each
  ordered system with unique individual identity)
• based on human (ordered sys.) preference for
  order identity
• disorder - messy, random, chaotic, uncorrelated,
  incoherent lacking identity
• with single identity (remaining numerous options
  without specific identity)
• given control volume within disorder does not
  have sustainable identity
• Sustainability of Localised Finite Gradient of
  Field Variables
• e.g. human as sustainable ordered system,
  temperature as field variable, temperature
  gradient w.r.t. disorder is maintained across
  sys. boundary
• disorder gradients - diminished

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Universal Basic Guiding Principles

• creation, stable existence total destruction
  of order from within disorder
• deduced from thermodynamic principles
• universally integrate order generating,
  sustaining, totally destroying processes, at
  all scales

Statement 1 (Creation of Order)

• As Localised Disequilibrium in Isolated System
  Increases Exceeds Particular Threshold,
  Sustainable Order is Created within Disorder
  whenever there is Chance
• Law of Maximum Entropy Production
• creation of sustainable order is not infinitely
  improbable
• Bertalanffy spontaneous order can appear in
  systems with energy flowing through them by their
  ability to build their order by dissipating
  potentials in their environments
• (1952) Problems of Life An Evaluation of Modern
  Biological Thought
• broken symmetry in creation of sustainable order
  net disorder
• net disorder is spontaneously (certainly)
  created
• creation of localised order is chance
  (uncertainty but possibility)
• Chance
• created by existing disorder probabilistically
  in dynamically unstable system
• refers to constraint/s being removed or minimal
  threshold/s reached, or coincidence
• e.g. minimal threshold of Earth cool enough so
  that its oceans would not evaporate, threshold
  oxygen in atm.
• Runnegar (1982) J. Geological Soc. Australia
• compliance with sustainability criterion

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Statement 2 (Creation of Order)

• In Isolated System, Created Order within
  Disorder is State of Higher Net Disorder than
  Preceding State of Total Disorder
• e.g. Q (disordered energy) rejected at lower
  temperature during Q ? W (ordered energy)
• Schroedinger sustainable orders like flames
  are permitted to exist away from equilibrium
  because they feed on negentropy in their
  environments
• (1945) What is Life? With Mind and Matter and
  Autobiographical Sketches
• Prigogine (1978) Science dissipative
  structures

Total Disorder
Order Disorder
Total Disorder
S
t
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Statement 3 (Existence of Order)

• In Isolated System, Order must Co-Exist with
  Disorder, but Disorder can Exist Alone as Total
  Disorder or Total Order does not Exist
• broken symmetry in existence of order disorder
  
• order created only locally in isolated system
• disorder created also without creating order
• Prigogine Stengers dissipative structures
• (1986) Order Out of Chaos Mans New Dialogue
  with Nature
• order cannot exist independently of their
  environment (disorder)
• low entropy values - low disorder
• order relative to disorder ? contrast with
  disorder

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Statement 4 (Existence of Order)

• In Isolated System, Order / or Disorder must
  Create More Order Disorder for Sustenance of
  Created Order else, Created Order is Converted
  in to Disorder
• broken symmetry in sustenance of order
  disorder
• (1) disorder exists by
• creating more disorder / creating order
  disorder / none of two (under equilibrium)
• (1) order exists only if
• it / or disorder create more order disorder
• (2) generation of disorder not necessarily
  accompanied by creation of order
• (2) creation of order is always in conjunction
  with disorder
• proof 3 exclusive choices available to order
• creation of additional order disorder
• creation of only disorder
• neither creation of order nor disorder
• single ordered sub-system cannot exist alone
• disorder alone cannot sustain created order
• events that do not support existence of order in
  disorder, are far more than those that support
  existence of order
• additional order must be created for existence
  of previously created order
• resulting events their sequence sustain order

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Statement 5 (Existence of Order)

• In Isolated System, Order can Create more Order
  only Through Disorder
• broken symmetry in creation of order disorder
• more order is created only thru interaction
  with disorder
• more disorder is generated through
• disorder alone
• conversion of order to disorder
• creation of order
• proof
• if order can create more order without any
  interaction with disorder ? order is localised
  isolated system

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Statement 6 (Total Destruction of Order)

• As Disorder of Isolated System Containing Order
  Increases Exceeds another Higher Threshold, all
  Order is Destroyed in to Total Disorder again if
  there is Chance
• surrounding disorder can also increase disorder
  further by destroying all order
• order can generate more disorder also by
  destroying order
• S gt Sthr ? individual orders work against other
  existing orders
• Law of Maximum Entropy Production
• if more entropy is generated by destroying all
  existing orders
• all existing orders destroyed in to disorder, if
  there is chance
• chance is probability that sustainability
  criterion for co-existence of order within
  disorder is not satisfied

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Statement 7 (Creation, Existence Total
Destruction of Order)

• In Isolated System, Creation, Existence Total
  Destruction of Order within Disorder is
  Sequential Train with Increasing Entropy
  Thresholds for Order Creation Total Destruction
  
• e.g. sequential train of formation, growth
  decay of coherent structures in chaotic turbulent
  flow
• Holmes et al. (1998) Turbulence, Coherent
  Structures, Dynamical Systems Symmetry

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Statement 8 (Existence of Order)

• In Isolated System, Disorder Exists Forever but
  Existence of Order is Fleeting
• broken symmetry in eternal existence
• disorder must exist whenever order exists
  (Statements 3,7)
• isolated system either comprises of only
  disorder, or order and disorder (7)

Statement 9 (Creation, Existence Total
Destruction of Order)

• In Isolated System, Role of Creation Fleeting
  Existence of Order is to increase System Entropy
  at Faster Rate than had Order not existed
• propagating loss in isolated system
• localised reversibilities in midst of
  irreversible processes
• higher order spontaneous process
• localised deviation from lower order spontaneity
  
• dramatic increase in rate at which potential is
  minimized in Bénard cell expt. in transition from
  disordered to ordered regime
• Swenson (2000) Annals New York Academy Sciences
• sd1 gt (sd1), (dsd1/dt) gt (dsd1/dt), (dsd1/dt)
  gt (dsd2/dt)

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Conceptual Model Exemplifying Order in Disorder
ISOLATED SYSTEM
Sub-System o1 (so1)
Surroundings w.r.t. Sub-systems sd(t)
Sub-system o2 (so2)
Sub-system oN (soN)

• GradF(t)o ? Grad(F)o,thr
• Sustainability Criterion
• sd(toN_c) gt sd(toN_c) gt sd(toN_c)

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Implications of Directives

• Order cannot be Sustained in Equilibrium
• Order is Unstable far away from Equilibrium
• Sustenance of Order within Disorder
• sustenance of fleeting disequilibrium
• sustainability - stability of order in disorder
• stability - continuous cyclic process/es in
  which order is involved to maintain its specific
  entropy level
• cyclic processes oscillate state of ordered
  sub-systems about equilibrium (with disorder)
• e.g. stability of ordered solar system - orbital
  motion of planets
• e.g. cyclic process of breathing / metabolism

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The Beginning S 0, i 1
Decision based on Law of Maximum Entropy
Production
Total Disorder

• Law of Maximum Entropy Production
• chooses direction that maximises entropy
  generation at given instant
• instantaneously chosen direction need not
  maximise entropy thereafter
• e.g. toN_c tot. destruction of order yields
  higher entropy production than sustenance
• subsequently entropy increase is slower (Stat. 9)

Is sd gt (sd) ?
No
Yes
Is Grad(F) lt Grad(F)thr?
No
Decision based on Sustainability Stability of
Order in Disorder
Yes
Order Disorder ?sd,oi_c so,i(toi_c) lt
so,thr (dsd,i/dt) gt (dsd,i/dt)
Additional block for alternative model Decision
based on threshold number of ordered sub-systems
Is i gt Nthr?
Yes
No
i i 1
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Conclusions Summary

• 9 Statements Basic Guiding Principles for
  Creation, Existence Total Destruction of Order,
  at all Scales.
• based on broken symmetry in nature in
  inter-convertibility of order disorder
  (addressed by Entropy Principle)
• creation destruction of order - decided by
  Entropy Principle, Law of Maximum Entropy
  Production, Sustainability Criterion
• Sustainability of Order
• result of one or more continuous cyclic process
  involving order
• Creation Existence of Ordered Systems
• higher order spontaneous process that results
  from localised deviation from lower order
  spontaneity
• Summary
• system non-linearity ? irreversibilities ?
  disorder
• disorder ? ? chaos ? (can create) sustainable
  order
• creation existence of order (non-linear) ? more
  disorder
• increased disorder ? eventually destroys all
  order ? total disorder
• Existing Order is neither Miracle, nor is it
  Purposeful Activity
• Natural Manifestation of Proposed Basic Guiding
  Principles

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Summary