Entropy production and transports in a conservative multibaker map with energy

For a previously introduced conservative multibaker map with energy, the Ga spard-Gilbert-Dorfman entropy production of the stationary slate induced by the flux boundary condition is calculated and the entropy production is sh own (i) to be nonnegative, (ii) to vanish in the fine-grained limit for fin ite chains, (iii) to take the phenomenologically expected value in the midd le of the chain and to deviate From it near the boundaries, and (iv) to red uce to the phenomenological expression in the scaling limit where the latti ce site n is an element of Z and time t is an element of Z are scaled respe ctively as n = LxiX and t = LtauT and the limits of L-xi --> +infinity and L-tau --> +infinity are taken while keeping the diffusion coefficient D = l L(tau)/L-xi(2) constant, I being the transition rate of the model. The mass and heat transports are also studied in the scaling limit under an additio nal assumption that the edges of the chain are in equilibrium with differen t temperatures. In the linear heat transport regime, Fourier's Law of heat conduction and t:he thermodynamic expression of the associated entropy prod uction are obtained.