Article
Entropy and Irreversibility in Noisy Non-Hamiltonian Systems
Physics Letters A
(1986)
Abstract
A previous dicussion of entropy and irreversibility in non-hamiltonian systems is extended to situations where noise is present, in which the generalized Liouville equation is replaced by a corresponding Fokker-Planck equation. The rate of change of entropy, Ṡ, is evaluated for an arbitrary choice of the volume element dV = γ(x)dx in the state space xH-theorem Ṡ ≥ 0 is obeyed only for the choice γ(x)=const×ϱ∞(x), where ϱ∞(x) is the statio solution of the Fokker-Planck equation. This choice seems natural and appropriate for general use, in contrast to the noise-free case where ϱ∞(x) is singular for systems with attractors. Systems may be classified as reversible or irreversible according to whether Ṡ.; does or does not tend to zero in the limit of zero noise.
Disciplines
Publication Date
August, 1986
DOI
10.1016/0375-9601(86)90733-4
Publisher Statement
At the time of publication John Ramshaw was affiliated with the Los Alamos National Laboratory.
Citation Information
J. D. Ramshaw, "Entropy and Irreversibility in Noisy Non-Hamiltonian Systems," Phys. Lett. A 117, 172 (1986).