Kinetic uncertainty relation on first-passage time for accumulated current

Abstract

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

Thermodynamic Uncertainty Relation for Time-Dependent Driving

“…Beyond considering the TUR as a tradeoff relation between precision and dissipation leading to bounds on the efficiency of biological processes or molecular machines [27][28][29] it has been established as a useful tool for inferring entropy production [30][31][32][33]. Hence, numerous attempts have been made to extend the range of applicability of the TUR including underdamped dynamics [34][35][36][37][38], ballistic transport between different terminals [39], heat engines [28,[40][41][42], periodic driving [43][44][45][46][47], stochastic field theories [48,49], generalizations to observables that are even under time-reversal [50][51][52], first-passage time problems [53][54][55] and quantum systems [39,[56][57][58][59][60][61][62][63].…”

Optimal thermodynamic uncertainty relation in Markov jump processes

“…Several numerical simulations [29,31] imply that KUR becomes a good bound in systems far from equilibrium. This shows clear contrast to the original TUR, which becomes a good bound in systems close to equilibrium.…”

“…The extension of the TUR has been discussed in various directions: One direction is to relax some assumptions on the setup of the TUR and generalize the inequality to a wider class of systems. Examples include systems with arbitrary initial states [16], systems with time-dependent driving [17], discrete-time processes [16,18,19], systems without time-reversal symmetry [11,20,21] including underdamped Langevin systems [10,[22][23][24], waiting-time statistics [25][26][27][28][29], and processes with unidirectional transitions [30]. Another direction is to replace the entropy production with other quantities such as activity [27,29,31] and probability current [30], which provide a new type of TUR-type inequalities.…”

“…Examples include systems with arbitrary initial states [16], systems with time-dependent driving [17], discrete-time processes [16,18,19], systems without time-reversal symmetry [11,20,21] including underdamped Langevin systems [10,[22][23][24], waiting-time statistics [25][26][27][28][29], and processes with unidirectional transitions [30]. Another direction is to replace the entropy production with other quantities such as activity [27,29,31] and probability current [30], which provide a new type of TUR-type inequalities. The short-time limit of the TUR [32][33][34][35] has also been discussed in the context of inference of entropy production [34,35].…”

Unified thermodynamic-kinetic uncertainty relation

“…The TUR imposes an upper bound on the precision of timeintegrated currents in terms of irreversible entropy production, indicating that increasing accuracy of currents has to pay a price in dissipation. In addition, the kinetic uncertainty relation (KUR), which is similar but different from the TUR, imposes another upper bound on the precision of generic counting observables in terms of dynamical activity [23,24,25]. These relations are not only theoretically important but also practically relevant; they can be applied to the thermodynamic inference of dissipation even in systems with hidden degrees of freedom [26,27,28,29].…”