Unified Thermodynamic Uncertainty Relations in Linear Response

Abstract

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium 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.

Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles

“…We now explore how to relate the diffusion coefficient to efficiency. Recent works have shown that, in nonequilibrium dynamics, the current fluctuations are bounded by the coarse-grained entropy production rate [37][38][39][40][41]. In active fluids, there is no average current of particles provided that no asymmetric external potential is applied [68][69][70].…”

“…While several works have strived to predict how internal transport is affected by activity [30][31][32][33][34][35], a recent study has put forward an explicit connection between diffusion and dissipation in a mixture of active and passive particles [36]. Moreover, for generic driven systems, it has been shown recently that the diffusion coefficient is generically bounded by dissipation [37][38][39][40][41]. Yet, this thermodynamic uncertainty relation (TUR) explicitly involves observable currents, thus being mostly useful for systems exhibiting directed transport.…”

Thermodynamic uncertainty relation in thermal transport

“…which is independent of temperature. Following the inequality (14), it is straightforward to show that the TUR is satisfied in the co-tunneling limit. In fact, the NESB model behaves similarly to the harmonic junction in the co-tunneling limit since ∆ > T ν .…”

Thermodynamic uncertainty relations in a linear system

“…A connection between discrete and continuous time uncertainty relations is shown in [34]. One can also see similar uncertainty relations in the context of discrete processes [35], multidimensional systems [36], Brownian motion in the tilted periodic potential [37], general Langevin systems [38], molecular motors [39], run and tumble processes [40], biochemical oscillations [41], interacting oscillators [42], effect of magnetic field [43], linear response [44], measurement and feedback control [45], information [46], underdamped Langevin dynamics [47], timedelayed Langevin systems [48], various systems [49], etc.. Recently, Hasegawa et al [50] found an uncertainty relation for the time-asymmetric observable for the system driven by a time-symmetric driving protocol using the steady state fluctuation theorem.…”