Dissipation-based uncertainty bounds for currents*

Markov jump processes can generate steady-state probability currents at the expense of dissipation. I will discuss how the dissipation also constraints the fluctuations in those currents. A small deviations corollary proves a "thermodynamic uncertainty principle"---to reduce the uncertainty in the estimate of nonequilibrium currents, a process must dissipate more. I will furthermore discuss corresponding dissipation-based uncertainty bounds for first passage time fluctuations.