Thermodynamic Uncertainty Relation for Time-Dependent Driving

Abstract

The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.

Thermodynamic uncertainty relation for underdamped dynamics driven by time-dependent protocols

“…There are many choices possible to give rise to different forms of TUR. In this study, we pursue one to lead to the TUR which relates the variance of Φ and the EP in the system and bath and to go to that for overdamped dynamics for large γ recently derived by Koyuk and Seifert [37].…”

The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

“…The form of ( 21) and (22) indicates the existence of a critical effective coupling parameter λ c eff below which the 'normal' ordering of time-scales breaks down, i.e., t EW→KPZ s > t KPZ c,s . One may think of this as shrinking the transient regime in Fig.…”

“…In regard of the latest achievements for the TUR see, e.g., [20][21][22][23][24]. In [25,26] these two areas have been connected by formulating a general field-theoretic TUR and evaluating it explicitly for the KPZ equation analytically as well as numerically in a certain scaling regime.…”

Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine

“…( 1) is smaller than 2. Involving quantum coherence [29], temporal driving [30][31][32], and magnetic field breaking time-reversal symmetry [26,33] will violate the original TUR.…”