On the well-posedness of equations for smoothed phase space distribution functions and irreversibility in classical statistical mechanics

Document Type

Article

Publication Date

6-8-2001

Abstract

We obtain an exact equation for a smoothed phase space distribution function for a system of N non-relativistic particles of unit mass obeying Hamiltonian dynamics. We show that this equation is well posed in only one time direction in the sense of the continuous dependence of the solution on the initial data. We interpret the ill-posedness of this equation in the backward time direction as the manifestation of irreversibility of the observable statistical quantities for systems obeying time-reversible dynamical laws.

Identifier

0035827490 (Scopus)

Publication Title

Journal of Physics A Mathematical and General

External Full Text Location

https://doi.org/10.1088/0305-4470/34/22/305

ISSN

03054470

First Page

4641

Last Page

4651

Issue

22

Volume

34

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