Multibaker map for shear flow and viscous heating.

A consistent description of shear flow and the accompanying viscous heating as well as the associated entropy balance is given in the framework of a deterministic dynamical system. The laminar shear flow is modeled by a Hamiltonian multibaker map which drives velocity and temperature fields. In the appropriate macroscopic limit one recovers the Navier-Stokes and heat conduction equations along with the associated entropy balance. This indicates that results of nonequilibrium thermodynamics can be described by means of an abstract, sufficiently chaotic, and mixing dynamics. A thermostating algorithm can also be incorporated into this framework.