We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross effects, in the framework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a second field with appropriate source terms is included in order to mimic, after coarse graining, a spatial temperature distribution and its time evolution. An expression is derived for the irreversible entropy production in a steady state, as the average of the growth rate of the relative density, a unique combination of the two fields.

• Received 17 February 1999

DOI:https://doi.org/10.1103/PhysRevE.61.R3295