Speed limit, dissipation bound and dissipation-time trade-off in thermal relaxation processes

We investigate bounds on speed, non-adiabatic entropy production and trade-off relation between them for classical stochastic processes with time-independent transition rates. Our results show that the time required to evolve from an initial to a desired target state is bounded from below by the informational-theoretic $\infty$-R\'enyi divergence between these states, divided by the total rate. Furthermore, we conjecture and provide extensive numerical evidence for an information-theoretical bound on the non-adiabatic entropy production and a novel dissipation-time trade-off relation that outperforms previous bounds in some cases.