Informatic entropy production rate from density field theories

A defining feature of non-equilibrium systems is the breakdown of time-reversal symmetry. Several approaches exist to quantify this breakdown, this talk will focus on computing the informatic entropy production rate, using the Onsager-Machlup path integral formulation, as a way to compute the probability of a given stochastic path. The approach presented here is applicable to a rather general set of stochastic equation, from the exact equation for microscopic densities (Dean-Kawasaki equation), to coarse-grained fluctuating hydrodynamics models with density-dependent mobility. We will show how a careful treatment of the so-called spurious drift, and proper time and space discretizations, we recover and generalize results obtained via other routes, such as ones from Doi-Peliti field theories. The quite direct computation presented in this talk indicates that it is possible to operate directly at the level of stochastic density consistently, which was not previously clear.