  The second law of thermodynamics states that entropy production cannot be
negative. Recent developments concerning uncertainty relations in stochastic
thermodynamics, such as thermodynamic uncertainty relations and speed limits,
have yielded refined second laws that provide lower bounds of entropy
production by incorporating information from current statistics or
distributions. In contrast, in this study, we bound the entropy production from
above by terms comprising the dynamical activity and maximum transition-rate
ratio. We derive two upper bounds: one applies to steady-state conditions,
whereas the other applies to arbitrary time-dependent conditions. We verify
these bounds through numerical simulation and identify several potential
applications.
