Entropy balance, time reversibility, and mass transport in dynamical systems

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Abstract
We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example.