Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss

2002/04/10 by Kenichiro Aoki, Aoki, Kenichiro, Dimitri Kusnezov +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0204015

5 pp, 3 figs

arxiv created 2002/04/10 · openalex publication_date 2002/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An explicit relation between the dimensional loss (ΔD), entropy production and transport is established under thermal gradients, relating the microscopic and macroscopic behaviors of the system. The extensivity of ΔD in systems with bulk behavior follows from the relation. The maximum Lyapunov exponents in thermal equilibrium and ΔD in non-equilibrium depend on the choice of heat-baths, while their product is unique and macroscopic. Finite size corrections are also computed and all results are verified numerically.

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• Remarks on non-Hamiltonian statistical mechanics: Lyapunov exponents and phase-space dimensionality loss

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