Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Abstract

Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and non-decreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

7 pages, 2 figures

References in corpus (16)

• The large deviation approach to statistical mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Fluctuations and response of nonequilibrium states
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Steady state statistics of driven diffusions
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• Universal Bound on the Fano Factor in Enzyme Kinetics
• Frenetic aspects of second order response
• Phase transitions in large deviations of reset processes
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models

Cited by in corpus (14)

• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Discrete-time thermodynamic uncertainty relation
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• First-passage times in renewal and nonrenewal systems
• Uncertainty relations for time-delayed Langevin systems
• Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
• Exploring quantum thermodynamics with NMR
• Thermodynamic uncertainty for run-and-tumble type processes
• Conflict Analysis and Resolution of Safety and Security Boundary Conditions for Industrial Control Systems
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Semi-Markov processes in open quantum systems: Connections and applications in counting statistics
• Concentration of Empirical First-Passage Times