A refined thermodynamic analysis of nonsecular master equations

• URL: http://arxiv.org/abs/2606.13504v1
• Date: Thu, 11 Jun 2026 15:52:40 GMT
• Title: A refined thermodynamic analysis of nonsecular master equations
• Abstract summary: We build a unified, consistent thermodynamic framework for nonsecular master equations.<n>We show that, unlike for secular master equations, the two entropy production rates differ because of the presence of non-vanishing stationary coherences.<n>We illustrate our results with a simple example, clarifying and completing the thermodynamic picture of Markovian dynamics in the quantum regime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a systematic thermodynamic analysis of nonsecular master equations. We consider master equations resulting either from the partial secular and the geometric-arithmetic approximations, two approximations ensuring the positivity of the system's dynamics when some of its transition frequencies are too small to enable the full secular approximation. Both cause the system to relax towards a steady state which is not the Gibbs state of its bare Hamiltonian. Nonetheless, we build a unified, consistent thermodynamic framework for those dynamics. Starting from a microscopic expression of the second law based on system-environment correlations, we employ a systematic perturbation theory to preserve the positivity of the second law despite the approximations done on the dynamics. We show that, in spite of the weak system-bath coupling, the system-bath interaction energy participates to the energy balance, as well as the Lamb-shift. Those extra contributions give rise to work performed by the system on the bath when the former is out of equilibrium. We compare this microscopic entropy production with the definition based on the contractivity of the reduced system dynamics (Spohn inequality). We show that, unlike for secular master equations, the two entropy production rates differ because of the presence of non-vanishing stationary coherences in the energy eigenbasis. However, in the case of a single thermal bath, the difference is purely transient, and no work can be cyclically extracted from the steady-state despite its non-Gibbs form. Finally, we illustrate our results with a simple example, clarifying and completing the thermodynamic picture of Markovian dynamics in the quantum regime.

Related papers

• Formulations of Quantum Thermodynamics and Applications in Open Systems [0.0]
  We explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy.<n>In this thesis, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions.<n>We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work.
  arXiv  Detail & Related papers  (2025-11-30T15:00:38Z)
• Thermalization and irreversibility of an isolated quantum system II [0.0]
  We numerically demonstrate irreversible growth of entanglement entropy caused by erasure of spread non-equilibrium state information.<n>Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective.
  arXiv  Detail & Related papers  (2025-06-02T06:13:25Z)
• Equilibrium and nonequilibrium steady states with the repeated interaction protocol: Relaxation dynamics and energetic cost [44.99833362998488]
  We study the dynamics of a qubit system interacting with thermalized bath-ancilla spins via a repeated interaction scheme.<n>Our key finding is that deterministic system-ancilla interactions do not typically result in the system thermalizing to the thermal state of the ancilla.
  arXiv  Detail & Related papers  (2025-01-09T17:35:36Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering [44.99833362998488]
  Floquet engineering is an important tool for realizing charge-neutral atoms in optical lattices. We show that a driven-dissipative system approximates a topological insulator.
  arXiv  Detail & Related papers  (2023-07-07T17:47:50Z)
• Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions [77.34726150561087]
  We deal with a generic time-local non-Markovian master equation. We define current and power to be process-dependent as in classical thermodynamics. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency.
  arXiv  Detail & Related papers  (2022-04-06T17:59:15Z)
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
  We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
  arXiv  Detail & Related papers  (2021-09-24T11:19:22Z)
• Fluctuation-dissipation relations for thermodynamic distillation processes [0.10427337206896375]
  fluctuation-dissipation theorem is a fundamental result in statistical physics. We first characterise optimal thermodynamic distillation processes. We then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system.
  arXiv  Detail & Related papers  (2021-05-25T08:53:19Z)
• Qubit thermodynamics far from equilibrium: two perspectives about the nature of heat and work in the quantum regime [68.8204255655161]
  We develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. We observe the appearance of a new term of work, which represents the energy cost of rotating the Bloch vector in presence of the external field that defines the local Hamiltonian. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.
  arXiv  Detail & Related papers  (2021-03-16T09:31:20Z)
• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics [0.0]
  We derive a master equation that accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. Our work paves the way for studying a variety of nanoscale quantum technologies including engines, refrigerators, or heat pumps.
  arXiv  Detail & Related papers  (2020-08-05T15:19:29Z)
• Assessing the role of initial correlations in the entropy production rate for non-equilibrium harmonic dynamics [0.0]
  We shed light on the relation between correlations, initial preparation of the system and non-Markovianity. We show that the global purity of the initial state of the system influences the behaviour of the entropy production rate.
  arXiv  Detail & Related papers  (2020-04-22T17:29:43Z)
• Out-of-equilibrium quantum thermodynamics in the Bloch sphere: temperature and internal entropy production [68.8204255655161]
  An explicit expression for the temperature of an open two-level quantum system is obtained. This temperature coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. We show that within this theoretical framework the total entropy production can be partitioned into two contributions.
  arXiv  Detail & Related papers  (2020-04-09T23:06:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.