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

Abstract

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.

Fission and Fusion Nuclear Reactions Second Law Analyses Based on Exergy Method

“…It is worth using the expressions above discussed for nuclear processes since energy and exergy are measurable properties. Moreover, the thermodynamic state of reference system behaving as a reservoir, can be arbitrarily selected being an auxiliary system only in the definition of thermodynamic entropy [8][9][10] and its components [14]. Hence, the calculation of entropy can be directly derived once thermodynamic states before and after nuclear reactions are defined.…”

Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

“… 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 ].…”

“…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 ].…”

“…The concept of equivalence and interconvertibility demonstrated by Gaggioli [ 25 , 26 , 27 ], further corroborates the need of entropy contributions specially defined for thermal, chemical and mechanical forms of energy and interaction. To do so, the definition of generalized thermodynamic entropy consists of the sum of terms expressing thermal, chemical and mechanical contributions of entropy property being extensive and additive for any system in any state [ 29 , 30 , 31 ]: where is the thermal entropy, or kinematic entropy, is the chemical entropy, or geometric entropy, and is the mechanical entropy characterizing, respectively, heat, mass and work interactions with useful external system and non-useful external reservoir. The physical meaning of these contributions can be clarified in relation to the microscopic model of the system constituted by a set of few particles or many particles in the framework of Statistical Physics perspective.…”