On the diffusive nature of entropy flow in infinite systems: Remarks to a paper by Guo-Papanicolau-Varadhan

The hydrodynamic behaviour of interacting diffusion processes is investigated by means of entropy (free energy) arguments. The methods of 13] are simplified and extended to infinite systems including a case of anharmonic oscillators in a degenerate thermal noise. Following 14, 15] and 3–5] we derive a priori bounds for the rate of entropy production in finite volumes as the size of the whole system is infinitely extended. The flow of entropy through the boundary is controlled in much the same way as energy flow in diffusive systems 4].This work was supported in part by the Hungarian National Foundation for Scientific Research Grant 1815, NSF Grant DMR 86-12369, and by the Institut des Hautes Etudes Scientifiques