Thermodynamic bounds on time-reversal asymmetry

Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our central result is a bound on the time-reversal asymmetry in terms of the total cycle affinity driving the system out of equilibrium. This result leads to further thermodynamic bounds on the asymmetry of directed fluxes; on the asymmetry of finite-time cross-correlations; and on the cycle affinity of coarse-grained dynamics.