Predictive statistical mechanics and macroscopic time evolution: hydrodynamics and entropy production

TL;DR

This paper extends a statistical mechanics framework based on maximum entropy principles to derive hydrodynamic equations and entropy production, demonstrating consistency with established thermodynamics and emphasizing the foundational role of predictive statistical mechanics in irreversibility.

Contribution

It generalizes previous models by incorporating hydrodynamic constraints, deriving entropy production in classical fluids, and reinforcing the foundational principles of predictive statistical mechanics.

Findings

Derived entropy production density for classical Hamiltonian fluids.

Showed consistency with nonequilibrium thermodynamics.

Highlighted the importance of maximum entropy principles for irreversibility.

Abstract

In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, leads to a definition of the rate of entropy change for closed Hamiltonian systems without any additional assumptions. Here, we generalize this basic model and, with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, show that the results obtained are consistent with the known results from the nonequilibrium statistical mechanics and thermodynamics of irreversible processes. In this way, as a part of the approach developed in this paper, the rate of entropy change and entropy production density for the classical Hamiltonian fluid are obtained. The results obtained suggest the general applicability of the foundational principles of predictive statistical mechanics and their importance for the theory of irreversibility.