Time correlations and the second entropy.

The authors study the transport of mass and heat in simulations of a Lennard-Jones fluid and demonstrate the calculation of transport coefficients, and of both the first and second entropies. These entropies are calculated from time correlation functions, as are the transport coefficients. They discuss the role of the second entropy in providing a physical explanation for the link between dynamic fluctuations and response. They illustrate the physical significance of the various contributions to the second entropy and how they simplify in the case of relaxation by steady-state flow. Certain approximations proposed for the calculation of the first entropy, common in the literature, are shown to break down under certain circumstances, and they give an improved method of calculation. They pay particular attention to the coupling between variables of opposite time parity in the transport matrix, and show that in general this cannot be neglected.