Theorem of Necessity and Sufficiency of Stable Equilibrium for Generalized Potential Equality between System and Reservoir

Palazzo, Pierfrancesco

doi:10.4236/jmp.2014.518196

Cited by 4 publications

(7 citation statements)

References 8 publications

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“…The present section describes the proof that generalized potential equality is a condition necessary and sufficient for stable equilibrium (or that stable equilibrium is a condition sufficient and necessary for generalized potential equality). This proof is included in a paper already published by the author [14] nevertheless is here again reported for sake of completeness and consistency as well as to better clarify the rationale behind the generalization of properties and principles here proposed.…”

Section: Necessity and Sufficiency Of Generalized Potential Equalitymentioning

confidence: 82%

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Palazzo¹

2016

JMP

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Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.

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Section: Necessity and Sufficiency Of Generalized Potential Equalitymentioning

confidence: 82%

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Palazzo¹

2016

JMP

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“…A further purpose would be that of proving both the necessity and sufficiency of stable equilibrium, already enunciated as a theorem for many-particle systems [14], also extended to few-particle systems adopting the same Beretta and Zanchini procedure to generalize the definition of thermodynamic entropy to any system, large and small, in any state, equilibrium and non-equilibrium.…”

Section: Discussionmentioning

confidence: 99%

A Method to Derive the Definition of Generalized Entropy from Generalized Exergy for Any State in Many-Particle Systems

Palazzo

2015

Entropy

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Abstract:The literature reports the proofs that entropy is an inherent property of any system in any state and governs thermal energy, which depends on temperature and is transferred by heat interactions. A first novelty proposed in the present study is that mechanical energy, determined by pressure and transferred by work interactions, is also characterized by the entropy property. The second novelty is that a generalized definition of entropy relating to temperature, chemical potential and pressure of many-particle systems, is established to calculate the thermal, chemical and mechanical entropy contribution due to heat, mass and work interactions. The expression of generalized entropy is derived from generalized exergy, which in turn depends on temperature, chemical potential and pressure of the system, and by the entropy-exergy relationship constituting the basis of the method adopted to analyze the available energy and its transfer interactions with a reference system which may be external or constitute a subsystem. This method is underpinned by the Second Law statement enunciated in terms of existence and uniqueness of stable equilibrium for each value of energy content of the system. The equality of chemical potential and equality of pressure are assumed, in addition to equality of temperature, to be necessary conditions for stable equilibrium.

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“… PMM2 is adopted in the proof of the entropy definition related to temperature, hence it is the definition of a thermal entropy property. Highest-(thermal)-entropy principle is applied to prove that stable equilibrium implies the equality of temperature, potential and pressure while thermal entropy determines thermal energy and heat interaction only, this representing a logical incompleteness and inconsistency thus introducing an incongruity [ 29 , 30 , 31 ]. To remove the incongruity, equality of temperature, potential and pressure have to imply thermal, chemical and mechanical equilibria and this opposite proof needs chemical entropy and mechanical entropy, in addition to thermal entropy, to assert a highest-generalized-entropy principle to be used in the proof [ 29 , 30 , 31 ].…”

Section: Considerations On Physical Aspect Of Second Law and Thermmentioning

confidence: 99%

“…Highest-(thermal)-entropy principle is applied to prove that stable equilibrium implies the equality of temperature, potential and pressure while thermal entropy determines thermal energy and heat interaction only, this representing a logical incompleteness and inconsistency thus introducing an incongruity [ 29 , 30 , 31 ].…”

Section: Considerations On Physical Aspect Of Second Law and Thermmentioning

confidence: 99%

“…To remove the incongruity, equality of temperature, potential and pressure have to imply thermal, chemical and mechanical equilibria and this opposite proof needs chemical entropy and mechanical entropy, in addition to thermal entropy, to assert a highest-generalized-entropy principle to be used in the proof [ 29 , 30 , 31 ].…”

Section: Considerations On Physical Aspect Of Second Law and Thermmentioning

confidence: 99%

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Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

Palazzo

2018

Entropy

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The present research aimed at discussing the thermodynamic and informational aspects of entropy concept to propose a unitary perspective of its definitions as an inherent property of any system in any state. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the Second Law, expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell's demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law.Entropy 2018, 20, 553 2 of 19 and its hierarchical structure associated to multi-scale system configuration; and (ii) the possibility (and, for a rigorous approach, the need) of extending to information science the generalization of foundations and properties in the thermodynamic domain with the aim of achieving a complete and consistent conceptual framework. The intent is here to highlight correlations among different facets of the theoretical and methodological building under elaboration by the community of physicists and information scientists.

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Theorem of Necessity and Sufficiency of Stable Equilibrium for Generalized Potential Equality between System and Reservoir

Cited by 4 publications

References 8 publications

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

A Method to Derive the Definition of Generalized Entropy from Generalized Exergy for Any State in Many-Particle Systems

Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

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