Entropy production of scalar Langevin systems

20 Aug 2020 - Irene

Motivated by the distinct non-equilibrium nature of active systems, we introduce the entropy production rate (EPR) as a quantitative measure of time reversal symmetry breaking. It can be defined either at particle level or at the level of coarse-grained fields such as den- sity; the EPR for the latter quantifies the extent to which these coarse-grained fields behave irreversibly. In this work, we first develop a general method to compute the EPR of scalar Langevin field theories with additive noise (this large class includes the aforementioned Model AB). Treating the scalar field φ as the sole observable, we arrive at an expression for the EPR that is non-negative for every field configuration and is quadratic in the time-antisymmetric component of the dynamics. Our general expression is a function of the quasipotential, which determines the full probability distribution for configurations, and is not generally calculable. To alleviate this difficulty, we present a small-noise expansion of the EPR, which only re- quires knowledge of the deterministic (mean-field) solution for the scalar field in steady state, which generally is calculable, at least numerically. We demonstrate this calculation for the case of Model AB. We then present a similar EPR calculation for Model AB with the con- servative and non-conservative contributions viewed as separately observable quantities. The results are qualitatively different, confirming that the field-level EPR depends on the choice of coarse-grained information retained within the dynamical description. For further details, see my paper on entropy production rate.