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.
Highlights
The literature reports that Second Law statement can be enunciated in terms of existence and uniqueness of sta-How to cite this paper: Palazzo, P. (2016) A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems
Stable equilibrium is proved to be a sufficient condition for equality of temperature, equality of potential and equality of pressure, or thermodynamic potentials, in many-particle systems interacting with an external reservoir R by heat, mass and work mutual exchange
Making reference to the statement formulated by Gyftopoulos and Beretta [2], the Highest-Generalized-Entropy Principle implies that among all states of a system characterized by given value of energy, number of constituents and parameters such as volume, there exist a unique stable equilibrium, according to Second Law statement here addressed to, and generalized entropy of this state is larger than the generalized entropy of any other state with the same value of energy, number of constituents and parameters
Summary
How to cite this paper: Palazzo, P. (2016) A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems. Palazzo ble equilibrium for a given value of energy content, compatible with a given composition of constituents and compatible with a given set of parameters of any system A This statement implies that each subsystem of a whole system has to be individually in stable equilibrium and that the composite of all subsystems mutually interacting with each other has to be in stable equilibrium as well. Potential and pressure are necessary conditions for stable equilibrium in addition to temperature; potential and pressure do not appear neither in the canonical expression of thermodynamic entropy, nor in the Highest Entropy Principle This logical inconsistency represents the outset of this research and its resolution is the objective to be achieved
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