Angelo Vulpiani — Universita' Sapienza, Roma #
Inferring Non-Equilibrium from Incomplete Information #
We discuss the problem of inferring the thermodynamic state of a system from partial observations. For a Gaussian process, we prove that it is impossible to distinguish an equilibrium system from an out-of-equilibrium one by observing a single variable unless a response experiment is performed. We show a possible way out when it is not possible to appropriately perturb the system to get the response but several observations recorded under different experimental conditions are available. We extend the discussion to Markov processes whose evolution is ruled by Langevin equations driven by a mixture of Gaussian and Poissonian white noises. These noises necessarily break the time-reversal symmetry, leading the system to non-equilibrium steady states for which the entropy production may be different from zero even for vanishing currents. We show that a direct measurement of entropy production is typically impractical but it is simpler and more robust to detect the time-reversal symmetry breaking by looking at higher order correlations and we provide analytical expressions in some cases. Finally we put it all together in order to analyze a real experiment on granular gases.