Predictive Statistical Mechanics and Macroscopic Time Evolution: Hydrodynamics and Entropy Production

• Published in: Foundations of physics Vol. 46; no. 7; pp. 891 - 914
• Main Author: Kuić, Domagoj
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-07-2016
• Subjects: Classical and Quantum Gravitation; Classical Mechanics; History and Philosophical Foundations of Physics; Philosophy of Science; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Statistical Physics and Dynamical Systems; Nonequilibrium theory; Thermodynamics of irreversible processes; Hydrodynamics; Maximum entropy principle; Hamiltonian dynamics; Statistical mechanics; Entropy production
• ISSN: 0015-9018; 1572-9516
• DOI: 10.1007/s10701-016-0009-8

In the previous papers (Kuić et al. in Found Phys 42:319–339,
2012
; Kuić 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.