Entropy production in the mesoscopic-leads formulation of quantum thermodynamics

Abstract

Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While there exist many techniques to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretised lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both non-interacting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semi-groups to infer the non-equilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.

11 pages, 6 figures. Final author version

References in corpus (16)

• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Markovian master equations for quantum thermal machines: local vs global approach
• Markovian Master Equations: A Critical Study
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Modeling heat transport through completely positive maps
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
• Relaxation-limited electronic currents in extended reservoir simulations
• Particle current statistics in driven mesoscale conductors
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths

Cited by in corpus (7)

• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Thermodynamics of photoelectric devices
• Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction coordinate approach
• Subtleties in the pseudomodes formalism
• Approaching the scaling limit of transport through lattices with dephasing