  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.
