Geometrical Bounds of the Irreversibility in Markovian Systems
arXiv:2005.02871 · doi:10.1103/PhysRevLett.126.010601
Abstract
We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from below by a modified Wasserstein distance between the initial and final states, thus strengthening the Clausius inequality in the reversible-Markov case. The modified metric can be regarded as a discrete-state generalization of the Wasserstein metric, which has been used to bound dissipation in continuous-state Langevin systems. Notably, the derived bounds can be interpreted as the quantum and classical speed limits, implying that the associated entropy production constrains the minimum time of transforming a system state. We illustrate the results on several systems and show that a tighter bound than the Carnot bound for the efficiency of quantum heat engines can be obtained.
arXiv comment7 pages, 1 figure; 15 pages of supplemental material with 1 figure
References in corpus (52)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Quantum Thermodynamics
- The role of quantum information in thermodynamics --- a topical review
- The maximum speed of dynamical evolution
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Eigenstate Thermalization Hypothesis
- Quantum heat engines and refrigerators: Continuous devices
- Quantum speed limit for physical processes
- Quantum speed limits in open system dynamics
- Single ion heat engine with maximum efficiency at maximum power
- Measuring thermodynamic length
- The quantum harmonic Otto cycle
- Thermodynamic metrics and optimal paths
- Universal trade-off relation between power and efficiency for heat engines
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Generalized Geometric Quantum Speed Limits
- Generalized Clausius inequality for nonequilibrium quantum processes
- Speed Limit for Classical Stochastic Processes
- Optimal protocols and optimal transport in stochastic thermodynamics
- Quantum equilibration in finite time
- Refined Second Law of Thermodynamics for fast random processes
- Quantum Speed Limits Across the Quantum-to-Classical Transition
- Quantum Speed Limit is Not Quantum
- A new class of transport distances
- Speed limit for open quantum systems
- Stochastic thermodynamic interpretation of information geometry
- Frenesy: time-symmetric dynamical activity in nonequilibria
- On the Mean Field and Classical Limits of Quantum Mechanics
- Thermodynamic Geometry of Microscopic Heat Engines
- Stochastic time-evolution, information geometry and the Cramer-Rao Bound
- Thermodynamic length in open quantum systems
- The length of time's arrow
- Work fluctuations in slow processes: quantum signatures and optimal control
- Lecture Notes on the Theory of Open Quantum Systems
- Quantum work statistics close to equilibrium
- Geometric quantum speed limits: a case for Wigner phase space
- A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
- Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations
- Quantum fluctuations hinder finite-time information erasure near the Landauer limit
- A dissipation bound for thermodynamic control
- Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence
- Quantum optimal transport with quantum channels
- Collective performance of a finite-time quantum Otto cycle
- Landauer's principle at zero temperature
- Information-theoretical bound of the irreversibility in thermal relaxation processes
- Nonequilibrium uncertainty principle from information geometry
- Geometrical bounds on irreversibility in open quantum systems
- Thermodynamic interpretation of Wasserstein distance
- Energy Dissipation Bounds for Autonomous Thermodynamic Cycles
- Information Geometry Aspects of Minimum Entropy Production Paths from Quantum Mechanical Evolutions
- Stochastic control in microscopic nonequilibrium systems
- Quantum detailed balance conditions and fluctuation relations for thermalizing quantum dynamics
Cited by in corpus (77)
- Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
- The Quantum Wasserstein Distance of Order 1
- Thermodynamics of Precision in Markovian Open Quantum Dynamics
- Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
- Finite-Time Quantum Landauer Principle and Quantum Coherence
- Geometric optimisation of quantum thermodynamic processes
- Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
- Observation of quantum strong Mpemba effect
- Unified thermodynamic-kinetic uncertainty relation
- Action quantum speed limits
- Learning quantum data with the quantum Earth Mover's distance
- Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
- Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks
- Speed Limits for Macroscopic Transitions
- Bounds in Nonequilibrium Quantum Dynamics
- Speed limit for a highly irreversible process and tight finite-time Landauer's bound
- Topological Speed Limit
- Housekeeping and excess entropy production for general nonlinear dynamics
- Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
- Collective advantages in finite-time thermodynamics
- Toward relaxation asymmetry: Heating is faster than cooling
- Geometric optimization of non-equilibrium adiabatic thermal machines and implementation in a qubit system
- Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
- Roadmap on Quantum Thermodynamics
- Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
- Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems
- Minimal Energy Cost to Initialize a Quantum Bit with Tolerable Error
- Finite-time Landauer principle beyond weak coupling
- Fundamental bounds on precision and response for quantum trajectory observables
- Extrapolating the thermodynamic length with finite-time measurements
- Thermodynamic speed limits for mechanical work
- Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
- Speed limits of the trace distance for open quantum system
- Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions
- Optimal finite-time heat engines under constrained control
- Improving the speed of variational quantum algorithms for quantum error correction
- Thermodynamic correlation inequality
- Quantum speed limit of a noisy continuous-variable system
- Quantum speed limits in arbitrary phase spaces
- Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport
- Lower bound for entropy production rate in stochastic systems far from equilibrium
- Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
- Inverse linear versus exponential scaling of work penalty in finite-time bit reset
- Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
- Relation between fluctuations and efficiency at maximum power for small heat engines
- Geometric characterization for cyclic heat engines far from equilibrium
- Fidelity-dissipation relations in quantum gates
- SLD Fisher information for kinetic uncertainty relations
- Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
- Infinite variety of thermodynamic speed limits with general activities
- Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
- Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics
- Minimum time connection between non-equilibrium steady states: the Brownian gyrator
- Force-current structure in Markovian open quantum systems and its applications: geometric housekeeping-excess decomposition and thermodynamic trade-off relations
- Thermodynamic concentration inequalities and tradeoff relations
- Classical shadows meet quantum optimal mass transport
- Speed limit, dissipation bound and dissipation-time trade-off in thermal relaxation processes
- Geometrical bounds on irreversibility in squeezed thermal bath
- Optimal synchronisation to a limit cycle
- Wasserstein Complexity of Quantum Circuits
- Generalized Entropic Quantum Speed Limits
- Bit reset protocols that obey activity-constrained speed limits do not minimize work for a given speed
- Active charge and discharge of a capacitor: scaling solution and energy optimization
- Wasserstein distance in speed limit inequalities for Markov jump processes
- Quasiprobability Thermodynamic Uncertainty Relation
- Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
- Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales
- A unified framework of unitarily residual measures for quantifying dissipation
- Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
- Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems
- Symmetry induced enhancement in finite-time thermodynamic trade-off relations
- Thermodynamic entropic uncertainty relation
- Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference
- Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps
- Critical Scaling of the Quantum Wasserstein Distance
- Time-cost-error trade-off relation in thermodynamics: The third law and beyond
- Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition