Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss

Details Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss

2002-04-10

arxiv.org/abs/nlin/0204015v1

Nonlinear Sciences

Chaotic Dynamics

5 pp, 3 figs

Scientific paper

An explicit relation between the dimensional loss ($\Delta D$), entropy production and transport is established under thermal gradients, relating the microscopic and macroscopic behaviors of the system. The extensivity of $\Delta D$ in systems with bulk behavior follows from the relation. The maximum Lyapunov exponents in thermal equilibrium and $\Delta D$ 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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