Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations

Abstract

Recent studies have revealed a deep connection between the asymmetry of cross-correlations and thermodynamic quantities in the short-time limit. In this study, we address the finite-time domain of the asymmetry for both open classical and quantum systems. Focusing on Markovian dynamics, we show that the asymmetry observed in finite-time cross-correlations is upper bounded by dissipation. We prove that, for classical systems in a steady state with arbitrary operational durations, the asymmetry exhibits, at most, linear growth over time, with the growth speed determined by the rates of entropy production and dynamical activity. In the long-time regime, the asymmetry exhibits exponential decay, with the decay rate determined by the spectral gap of the transition matrix. Remarkably, for quantum cases, quantum coherence is equally important as dissipation in constraining the asymmetry of correlations. We demonstrate an example where only quantum coherence bounds the asymmetry while the entropy production rate vanishes. Furthermore, we generalize the short-time bounds on correlation asymmetry, as reported by Shiraishi [Phys. Rev. E 108, L042103 (2023)] and Ohga et al. [Phys. Rev. Lett. 131, 077101 (2023)], to encompass finite-time scenarios. These findings offer novel insights into the thermodynamic aspects of correlation asymmetry.

21 pages, 3 figures

References in corpus (22)

• Thermodynamic uncertainty relation for biomolecular processes
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Odd Viscosity and Odd Elasticity
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Thermodynamics of Gambling Demons
• Unified thermodynamic-kinetic uncertainty relation
• Thermodynamic Bound on the Asymmetry of Cross-Correlations
• Time reversal symmetry breaking and odd viscosity in active fluids: Green-Kubo and NEMD results
• Quantum Speed Limits for Observables
• Quantum speed limits on operator flows and correlation functions
• Toward relaxation asymmetry: Heating is faster than cooling
• Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
• Maximal power for heat engines: role of asymmetric interaction times
• Dynamic and thermodynamic bounds for collective motor-driven transport
• Entropy production limits all fluctuation oscillations
• Thermodynamic correlation inequality
• Dissipative timescales from coarse-graining irreversibility
• Exploring the role of asymmetric-pulse modulation in quantum thermal machines and quantum thermometry

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• Wasserstein distance in speed limit inequalities for Markov jump processes
• Information geometric bound on general chemical reaction networks
• Compensating random transition-detection blackouts in Markov networks
• Quasiprobability Thermodynamic Uncertainty Relation
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference