Steepest-Entropy-Ascent Irreversible Relaxation Towards Thermodynamic Equilibrium: The Dynamical Ansatz that Completes the Gyftopoulos-Hatsopoulos Unified Theory with a General Quantal Law of Causal Evolution

Authors : Gian Paolo BERETTA

Pages : 117-128

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Publication Date : 2006-09-01

Article Type : Research Paper

Abstract :We overview the main features of the general equation of motion that completes the Gyftopoulos-Hatsopoulos unified theory of mechanics and thermodynamics with a quantal law of causal evolution that entails relaxation towards stable equilibrium for any non-equilibrium state, no matter how far from thermodynamic equilibrium. We illustrate with numerical examples the behavior of the equation of motion by discussing spontaneous energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels ei and i = 1, 2,…, N. For this system the time-dependent occupation probabilities piinsert ignore into journalissuearticles values(t); obey the nonlinear rate equations which include functions of the piinsert ignore into journalissuearticles values(t);’s that maintain invariant the mean energy and the normalization condition. The entropy is a non-decreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions of the rate equations are unique and well-defined for arbitrary initial conditions piinsert ignore into journalissuearticles values(0); and for all times, -∞ Keywords : Gyftopoulos Hatsopoulos unified quantum theory of mechanics and thermodynamics, quantal law of causal evolution, irreversible relaxation towards stable equilibrium, ancestral or primordial lowest entropy state, existence and uniqueness

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