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arXiv:2404.15915 · The Journal of Chemical Physics

Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

Devvrat Tiwari, Baibhab Bose, Subhashish Banerjee

Published Mar 17, 2025• 15 citations
arXivHTMLPDF

Abstract

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.

DOI
10.1063/5.0254029

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The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.
We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1l_1l1​-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.
In this work, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.
We analyze here through exact calculations the thermodynamical effects in depolarizing a quantum spin-bath initially at zero temperature through a quantum probe coupled to an infinite temperature bath by evaluating the heat and entropy changes. We show that the correlations induced in the bath during the depolarizing process does not allow for the entropy of the bath to increase towards its maximal limit. On the contrary, the energy deposited in the bath can be completely extracted in a finite time. We explore these findings through an exactly solvable central spin model, wherein a central spin-1/2 system is homogeneously coupled to a bath of identical spins. Further, we show that, upon destroying these unwanted correlations, we boost the rate of both energy extraction and entropy towards their limiting values. We envisage that these studies are relevant for quantum battery research wherein both charging and discharging processes are key to characterizing the battery performance.
Recently, there has been an upsurge of interest in quantum thermodynamic devices, notably quantum batteries. Quantum batteries serve as energy storage devices governed by the rules of quantum thermodynamics. Here, we propose a model of a quantum battery wherein the system of interest can be envisaged as a battery, and the ambient environment acts as a charger (dissipation) mechanism, modeled along the ubiquitous quantum Brownian motion. We employ quantifiers such as ergotropy and its (in)coherent manifestations, as well as instantaneous and average powers, to characterize the performance of the quantum battery. We investigate the influence of the bath's temperature and the system's coupling with the environment via momentum and position coordinates on the discharging and recharging dynamics. Moreover, we probe the memory effects of the system's dynamics and obtain a relationship between the system's non-Markovian evolution and the battery's recharging process.
Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While many techniques exist 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 discretized 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 noninteracting 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 semigroups to infer the nonequilibrium 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.