Irreversibility, Loschmidt echo, and thermodynamic uncertainty relation

Abstract

Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.

arXiv comment7 pages, 2 figures; 10 pages of supplemental material with 3 figures

References in corpus (53)

• Thermodynamic uncertainty relation for biomolecular processes
• Quantum Fisher information matrix and multiparameter estimation
• Dissipation bounds all steady-state current fluctuations
• Dynamics of Loschmidt echoes and fidelity decay
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Quantum Trajectories and Quantum Measurement Theory
• Fluctuation theorem uncertainty relation
• Quantifying dissipation using fluctuating currents
• Loschmidt Echo
• Current fluctuations and transport efficiency for general Langevin systems
• Thermodynamics of precision in quantum non equilibrium steady states
• Generic Properties of Stochastic Entropy Production
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Thermodynamic uncertainty relation for time-dependent driving
• Inferring entropy production from short experiments
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
• Multidimensional thermodynamic uncertainty relations
• Quantum thermodynamic uncertainty relation for continuous measurement
• Uncertainty relations in stochastic processes: An information inequality approach
• Entropy production along nonequilibrium quantum jump trajectories
• Estimating entropy production by machine learning of short-time fluctuating currents
• Kinetic uncertainty relation
• Autonomous quantum clocks: does thermodynamics limit our ability to measure time?
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Time-information uncertainty relations in thermodynamics
• Entropy production estimation with optimal current
• Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Dynamical phase transitions as a resource for quantum enhanced metrology
• Thermodynamic uncertainty relation for general open quantum systems
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Qubit models of weak continuous measurements
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Bounds on current fluctuations in periodically driven systems
• Thermodynamic uncertainty relation in thermal transport
• Uncertainty relations for underdamped Langevin dynamics
• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• Fisher information and asymptotic normality in system identification for quantum Markov chains
• Thermodynamic uncertainty relations under arbitrary control protocols
• Thermodynamic Uncertainty Relations for Bosonic Otto Engines
• Thermodynamic uncertainty relation in atomic-scale quantum conductors
• Quantum Estimation via Sequential Measurements
• Quantum Estimation by Local Observables
• Scalable Information Inequalities for Uncertainty Quantification
• Joint statistics of work and entropy production along quantum trajectories
• On Relations Between the Relative entropy and ${\chi }^2$-Divergence, Generalizations and Applications
• Hypothesis testing with open quantum systems
• Joint fluctuation theorems for sequential heat exchange

Cited by in corpus (17)

• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Unified thermodynamic-kinetic uncertainty relation
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine
• Pareto-optimal cycles for power, efficiency and fluctuations of quantum heat engines using reinforcement learning
• Role of Quantum Coherence in Kinetic Uncertainty Relations
• Absence and recovery of cost-precision tradeoff relations in quantum transport
• Thermodynamic uncertainty relation for quantum first passage process
• Thermodynamic correlation inequality
• Exact solution to quantum dynamical activity
• A tensor network approach to sensing quantum light-matter interactions
• Speed limits and thermodynamic uncertainty relations for quantum systems governed by non-Hermitian Hamiltonian
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• SLD Fisher information for kinetic uncertainty relations
• Violation of the thermodynamic uncertainty relation in quantum collisional models
• Universal Precision Limits in General Open Quantum Systems
• Detecting quantumness with generalized Loschmidt echoes