Variational formula for the current generating function and finite-time thermodynamic uncertainty relations

Sep 4, 2017, 3:40 PM


oral Session 2


Andreas Dechant (Kyoto University)


Bounds on the current generating function for stochastic dynamics and the thermodynamic uncertainty relations that follow from them have recently attracted much attention. Here, we focus on the space-time continuous case of Langevin dynamics. We derive a variational formula for the generating function of a generalized current, which is valid at finite time, extending the previously known results for the long-time limit. We show that the proof of the recently proposed finite-time thermodynamic uncertainty relation follows from the variational formula in a straightforward way. This relation provides a universal bound on any current in a non-equilibrium steady state in terms of the entropy production. We also discuss possible extensions to the transient case and to systems with time-dependent driving.

Primary author

Andreas Dechant (Kyoto University)


Shin-ichi Sasa (Kyoto University)

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