Coarse-grained entropy and information dimension of dynamical systems: The driven Lorentz gas.
We study the resolution dependence of the steady-state saturation values of coarse-grained entropies characterizing general dynamical systems. For dissipative maps they are proportional to the information codimension of the chaotic attractor. Thus, they provide a highly accurate method for determining the information dimension and related characteristics of the dynamical system. This general result is demonstrated for the field-driven Lorentz gas. In the discussion, we take the results on the resolution dependence of the entropy as the starting point to revisit different approaches to define thermodynamic entropy production for transport processes in dynamical systems, and discuss the role of local equilibrium in this enterprise.
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium. juergen.vollmer@physik.uni-marburg.de
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