Predictive statistical mechanics and macroscopic time evolution. A model for closed Hamiltonian systems

TL;DR

This paper develops a predictive statistical mechanics model for closed Hamiltonian systems, using information theory and the Liouville equation to describe macroscopic time evolution without extra assumptions.

Contribution

It introduces a novel approach applying maximum entropy principles to Hamiltonian dynamics, linking microscopic information loss to macroscopic entropy change.

Findings

Maximizes conditional information entropy under Liouville constraint

Defines entropy rate without additional assumptions

Connects microscopic dynamics to macroscopic evolution

Abstract

Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic time evolution of the system in the case of incomplete information about the microscopic dynamics was considered. In the model of a closed Hamiltonian system (i.e. system that can exchange energy but not particles with the environment) that with the Liouville equation uses the concepts of information theory, analysis was conducted of the loss of correlation between the initial phase space paths and final microstates, and the related loss of information about the state of the system. It is 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 change of entropy without any additional assumptions. In the subsequent paper (http://arxiv.org/abs/1506.02625) this basic model is generalized further and brought into direct connection with the results of nonequilibrium theory.