Equivalence of Irreversible Entropy Production in Driven Systems: An Elementary Chaotic Map Approach

A multibaker map is generalized in order to mimic the thermostating algorithm of transport models. Elementary calculations yield the irreversible entropy production caused by coarse graining of the phase-space density. For different systems, either in steady states (periodic or flux boundaries) or subjected to absorbing boundaries, the specific irreversible entropy production is shown to be $u^2/D$, where $u$ denotes the local streaming velocity (current per density) and $D$ is the diffusion coefficient.