Optimal thermodynamic uncertainty relation in Markov jump processes

Abstract

We investigate the tightness and optimality of thermodynamic-uncertainty-relation (TUR)-type inequalities from two aspects, the choice of the Fisher information and the class of possible observables. We show that there exists the best choice of the Fisher information, given by the pseudo entropy production, and all other TUR-type inequalities in a certain class can be reproduced by this tightest inequality. We also demonstrate that if we observe not only generalized currents but generalized empirical measures, the TUR-type inequality becomes optimal in the sense that it achieves its equality in general nonequilibrium stationary systems. Combining these results, we can draw a hierarchical structure of TUR-type inequalities.

13 pages, no figure

References in corpus (17)

• Thermodynamic uncertainty relation for biomolecular processes
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuations and response of nonequilibrium states
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Discrete-time thermodynamic uncertainty relation
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Steady state statistics of driven diffusions
• Hierarchical Bounds on Entropy Production Inferred from Partial Information
• Improving thermodynamic bounds using correlations
• Role of measurement-feedback separation in autonomous Maxwell's demons
• Universal form of thermodynamic uncertainty relation for Langevin dynamics
• Higher-order Efficiency Bound and Its Application to Nonlinear Nano-thermoelectrics
• Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Thermodynamic uncertainty relation for underdamped dynamics driven by time-dependent protocols

Cited by in corpus (13)

• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
• Unified thermodynamic-kinetic uncertainty relation
• Direct Route to Thermodynamic Uncertainty Relations and Their Saturation
• Housekeeping and excess entropy production for general nonlinear dynamics
• Estimating Entropy Production Rates with First-Passage Processes
• Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state
• Thermodynamic Uncertainty Relations for Steady-State Thermodynamics
• Entropy of Sharp Restart
• Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies
• Fluctuation-response relation of time-symmetric quantities around general nonequilibrium stationary state