Uncertainty relation under information measurement and feedback control

Abstract

Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the amount of information obtained from the measurements. We prove that the entropy production and the information quantity constrain from below the fluctuation of arbitrary observables that are antisymmetric under time reversal. The information term is the sum of the mutual entropy production and the Kullback--Leibler divergence, which characterises the irreversibility of the measurement outcomes. The result holds for finite observation times and for both continuous- and discrete-time systems. We apply the derived relation to study the precision of a flashing Brownian ratchet.

19 pages, 4 figures

References in corpus (52)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Nonequilibrium Thermodynamics of Feedback Control
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Thermodynamics with continuous information flow
• Fluctuation theorem uncertainty relation
• Thermodynamic uncertainty relations from exchange fluctuation theorems
• Information-theoretic approach to the study of control systems
• Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell's demon interpretation
• Information-Theoretic Limits of Control
• Current fluctuations and transport efficiency for general Langevin systems
• Discrete-time thermodynamic uncertainty relation
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Universal bound on the efficiency of molecular motors
• Cycling tames power fluctuations near optimum efficiency
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• Second-law-like inequalities with information and their interpretations
• Uncertainty relations in stochastic processes: An information inequality approach
• Thermodynamic Reversibility in Feedback Processes
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Unifying Three Perspectives on Information Processing in Stochastic Thermodynamics
• Tightening the uncertainty principle for stochastic currents
• Feedback control in a collective flashing ratchet
• Energetic costs, precision, and efficiency of a biological motor in cargo transport
• Thermodynamic uncertainty relations including measurement and feedback
• Bounds on current fluctuations in periodically driven systems
• Universal Bound on the Fano Factor in Enzyme Kinetics
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Uncertainty relations for underdamped Langevin dynamics
• Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials
• Multipartite information flow for multiple Maxwell demons
• Information and flux in a feedback controlled Brownian ratchet
• Exact symmetries in the velocity fluctuations of a hot Brownian swimmer
• Mapping of uncertainty relations between continuous and discrete time
• Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes
• Closed-loop control strategy with improved current for a flashing ratchet
• Information and maximum power in a feedback controlled Brownian ratchet
• Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control
• Mapping current fluctuations of stochastic pumps to nonequilibrium steady states
• Thermodynamic uncertainty relation for time-delayed Langevin systems
• Uncertainty relations for time-delayed Langevin systems
• Exact results for the finite time thermodynamic uncertainty relation
• Thermodynamic uncertainty for run-and-tumble type processes

Cited by in corpus (27)

• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Estimating entropy production by machine learning of short-time fluctuating currents
• Entropy production estimation with optimal current
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Thermodynamic uncertainty relations under arbitrary control protocols
• Experimental study of the thermodynamic uncertainty relation
• Thermodynamic uncertainty relations for coherently driven open quantum systems
• Thermodynamic Uncertainty Relations for Bosonic Otto Engines
• Kinetic uncertainty relation on first passage time for accumulated current
• Maxwell's demon in a double quantum dot with continuous charge detection
• Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
• Thermodynamic uncertainty relation for energy transport in transient regime -- Model study
• Reaching and violating thermodynamic uncertainty bounds in information engines
• Explicit solution of the generalised Langevin equation
• Exploring quantum thermodynamics with NMR
• Improved bound on entropy production in a quantum annealer
• Multilevel quantum thermodynamic swap engines
• A thermodynamic uncertainty relation for a system with memory
• Universal bounds on the performance of information-thermodynamic engine
• Effective Entropy Production and Thermodynamic Uncertainty Relation of Active Brownian Particles
• Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature
• Detailed fluctuation theorem bounds apparent violations of the second law
• Information in feedback ratchets
• Thermodynamic uncertainty relations in a linear system
• Markovian description of a wide class of feedback-controlled systems: Application to the feedback flashing ratchet
• Universal Precision Limits in General Open Quantum Systems