  Nonequilibrium processes break time-reversal symmetry and generate entropy.
Living systems are driven out-of-equilibrium at the microscopic level of
molecular motors that exploit chemical potential gradients to transduce free
energy to mechanical work, while dissipating energy. The amount of energy
dissipation, or the entropy production rate (EPR), sets thermodynamic
constraints on cellular processes. Practically, calculating the total EPR in
experimental systems is challenging due to the limited spatiotemporal
resolution and the lack of complete information on every degree of freedom.
Here, we propose a new inference approach for a tight lower bound on the total
EPR given partial information, based on an optimization scheme that uses the
observed transitions and waiting times statistics. We introduce hierarchical
bounds relying on the first- and second-order transitions, and the moments of
the observed waiting time distributions, and apply our approach to two generic
systems of a hidden network and a molecular motor, with lumped states. Finally,
we show that a lower bound on the total EPR can be obtained even when assuming
a simpler network topology of the full system.
