Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction (Q2924901)

The authors study some stochastic processes which are used to describe the heat conduction, in which a local internal energy is exchanged through random nearest-neighbour interactions. Three basic such stochastic processes are considered: the Brownian momentum process, the Brownian energy process with parameter \(m\), and the Kipnis-Marchioro-Presutti process. For each model, they study the equilibrium properties, the hydrodynamic limit and the corresponding large deviation principle. Comparing these results suggests some implications on the corresponding structures.