The Thermo-Kinetic Relations

Abstract: Thermo-Kinetic relations bound thermodynamic quantities such as entropy production with statistics of dynamical observables. We introduce a Thermo-Kinetic Relation to bound the entropy production or the non-adiabatic (Hatano-Sasa, excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and non stationary distributions. For stationary cases, this bound is akin to a Thermodynamic Uncertainty Relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For non-stationary cases, this bound generalises Classical Speed Limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a trade-off between non-adiabatic entropy production and housekeeping entropy production: the latter can be increased in order to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our Thermo-Kinetic Relations on simple examples from biophysics and computing devices.