Generalized time-reversal symmetry and effective theories for nonequilibrium matter

The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. In this talk, I will describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium systems. This approach applies to a range of examples, including nonreciprocal (predator-prey) dynamics, dissipative and driven rigid-body motion, and active chiral fluids and solids. Many of these systems exhibit a generalized time-reversal symmetry, which plays a crucial role within our formalism, and which in many cases can be implemented within the Martin-Siggia-Rose path integral. This effective theory formalism yields generalizations of the fluctuation-dissipation theorem and the second law of thermodynamics valid out of equilibrium. By stipulating a stationary distribution and a set of symmetries—rather than postulating the stochastic equations of motion directly—the effective theory framework provides an alternative route to building phenomenological models of driven and active matter.