Abstract

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in non-equilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic non-equilibrium processes. Here we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including for example ballistic transport, and periodically driven classical and quantum systems. We find that for broken time-reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics it reveals a connection between the TUR and current fluctuation theorems.

arxiv:1803.01904 (accepted by Phys. Rev. Lett.)