Entropy Production and Transports in a Conservative Multibaker Map with Energy

Abstract

For a previously introduced conservative multibaker map with energy, the Gaspard–Gilbert–Dorfman entropy production of the stationary state induced by the flux boundary condition is calculated and the entropy production is shown (i) to be nonnegative, (ii) to vanish in the fine-grained limit for finite chains, (iii) to take the phenomenologically expected value in the middle of the chain and to deviate from it near the boundaries, and (iv) to reduce to the phenomenological expression in the scaling limit where the lattice site n∈Z and time t∈Z are scaled respectively as n=L _ξ X and t=L _τ T and the limits of L _ξ→+∞ and L _τ→+∞ are taken while keeping the diffusion coefficient D=lL _τ/L ² _ξ constant, l being the transition rate of the model. The mass and heat transports are also studied in the scaling limit under an additional assumption that the edges of the chain are in equilibrium with different temperatures. In the linear heat transport regime, Fourier's law of heat conduction and the thermodynamic expression of the associated entropy production are obtained.