Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss

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.