  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.
