Unified Thermodynamic Uncertainty Relations in Linear Response

Macieszczak, Katarzyna; Brandner, Kay; Garrahan, Juan P.

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 unified 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 find 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.

Citation

Macieszczak, K., Brandner, K., & Garrahan, J. P. (2018). Unified Thermodynamic Uncertainty Relations in Linear Response. Physical Review Letters, 121(13), Article 130601. https://doi.org/10.1103/physrevlett.121.130601

• Journal Article Type: Article
• Acceptance Date: Sep 3, 2018
• Online Publication Date: Sep 24, 2018
• Publication Date: Sep 28, 2018
• Deposit Date: Sep 5, 2018
• Publicly Available Date: Sep 5, 2018
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 121
• Issue: 13
• Article Number: 130601
• DOI: https://doi.org/10.1103/physrevlett.121.130601
• Public URL: https://nottingham-repository.worktribe.com/output/1060418
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.130601
• Contract Date: Sep 5, 2018