Full counting statistics and coherences: fluctuation symmetry in heat transport with the Unified quantum master equation
arXiv:2212.11307 · doi:10.1103/PhysRevE.107.054115
Abstract
Recently, a "Unified" quantum master equation was derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form. This equation describes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the Unified quantum master equation to investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equation gives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the Unified equation is simultaneously thermodynamically consistent and more accurate than the fully Secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the Unified equation to those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the Secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential for the properly capturing the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.
15 pages, 7 figures
References in corpus (30)
- Thermodynamic uncertainty relation for biomolecular processes
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- Markovian master equations for quantum thermal machines: local vs global approach
- Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
- Testing the validity of the local and global GKLS master equations on an exactly solvable model
- Preservation of Positivity by Dynamical Coarse-Graining
- Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
- Coherence-enhanced efficiency of feedback-driven quantum engines
- Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
- Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
- Thermodynamics of Precision in Markovian Open Quantum Dynamics
- Long-lived quasi-stationary coherences in V-type system driven by incoherent light
- Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
- A thermodynamically consistent Markovian master equation beyond the secular approximation
- Quantum thermodynamically consistent local master equations
- Steady quantum coherence in non-equilibrium environment
- Coherences and the thermodynamic uncertainty relation: Insights from quantum absorption refrigerators
- Optimizing autonomous thermal machines powered by energetic coherence
- Thermodynamic consistency of quantum master equations
- Strong coupling effects in quantum thermal transport with the reaction coordinate method
- Canonically consistent quantum master equation
- The role of quantum coherence in energy fluctuations
- Quantum Thermodynamics with Degenerate Eigenstate Coherences
- Violations of the second law of thermodynamics by a non completely positive dynamics
- Quantum coherence-control of thermal energy transport: The V model as a case study
- Noise-Induced Coherence in Molecular Processes
- Perturbative Steady States of Completely Positive Quantum Master Equations
- Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate
- Compact and complete description of non-Markovian dynamics
- Thermodynamics of the Coarse-Graining Master Equation
Cited by in corpus (10)
- Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
- Hyper-acceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment
- Role of Quantum Coherence in Kinetic Uncertainty Relations
- Searching for Lindbladians obeying local conservation laws and showing thermalization
- Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
- Understanding and Generalizing Unique Decompositions of Generators of Dynamical Semigroups
- Random walks on modular chains: Detecting structure through statistics
- Quasi-probability distribution of work in a measurement-based quantum Otto engine
- Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
- Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations