  Complex physical dynamics can often be modeled as a Markov jump process
between mesoscopic configurations. When jumps between mesoscopic states are
mediated by thermodynamic reservoirs, the time-irreversibility of the jump
process is a measure of the physical dissipation. We rederive a recently
introduced inequality relating the dissipation rate to current fluctuations in
jump processes. We then adapt these results to diffusion processes via a
limiting procedure, reaffirming that diffusions saturate the inequality.
Finally, we study the impact of spatial coarse-graining in a two-dimensional
model with driven diffusion. By observing fluctuations in coarse-grained
currents, it is possible to infer a lower bound on the total dissipation rate,
including the dissipation associated with hidden dynamics. The tightness of
this bound depends on how well the spatial coarse-graining detects dynamical
events that are driven by large thermodynamic forces.
