TITLE:
Theorem of Necessity and Sufficiency of Stable Equilibrium for Generalized Potential Equality between System and Reservoir
AUTHORS:
Pierfrancesco Palazzo
KEYWORDS:
Available Energy, Second Law, Stable Equilibrium, Nonequilibrium, Generalized Exergy, Generalized Entropy, Generalized Potential
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.18,
December
10,
2014
ABSTRACT: The
literature reports that equality of temperature, equality of potential and
equality of pressure between a system and a reservoir are necessary conditions
for the stable equilibrium of the system-reservoir composite or, in the
opposite and equivalent logical inference, that stable equilibrium is a
sufficient condition for equality. The aim and the first novelty of the present
study is to prove that equality of temperature, potential and pressure is also
a sufficient condition for stable equilibrium, in addition to necessity,
implying that stable equilibrium is a condition also necessary, in addition to
sufficiency, for equality. The second novelty is that the proof of the
sufficiency of equality (or the necessity of stable equilibrium) is attained by
means of the generalization of the entropy property, derived from the
generalization of exergy property, which is used to demonstrate that stable
equilibrium is a logical consequence of equality of generalized potential. This
proof is underpinned by the Second Law statement and the Maximum-Entropy
Principle based on generalized entropy which depends on temperature, potential
and pressure of the reservoir. The conclusion, based on these two novel
concepts, consists of the theorem of necessity and sufficiency of stable
equilibrium for equality of generalized potentials within a composite
constituted by a system and a reservoir.