Canonical quantization for Equilibrium Thermodynamics

• URL: http://arxiv.org/abs/2511.14121v1
• Date: Tue, 18 Nov 2025 04:12:25 GMT
• Title: Canonical quantization for Equilibrium Thermodynamics
• Authors: Luis F. Santos, Victor Hugo M. Ramos, Danilo Cius, Mario C. Baldiotti, Bárbara Amaral,
• Abstract summary: We formulate a canonical quantization of Equilibrium Thermodynamics by applying Dirac's theory of constrained systems.<n>For the ideal gas, a Schrdinger-like equation emerges in which entropy plays the role of time, and the wave function acquires a phase determined by the internal energy.<n>A pseudo-Hermitian framework restores Hermiticity of the temperature operator and establishes the equivalence among constraint realizations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We formulate a canonical quantization of Equilibrium Thermodynamics by applying Dirac's theory of constrained systems. Thermodynamic variables are treated as conjugate pairs of coordinates and momenta, allowing extensive and intensive quantities to be promoted to operators in a Hilbert space. The formalism is applied to the ideal gas, the van der Waals gas, and the photon gas, illustrating both first- and second-class quantization procedures. For the ideal gas, a Schrödinger-like equation emerges in which entropy plays the role of time, and the wave function acquires a phase determined by the internal energy. A pseudo-Hermitian framework restores Hermiticity of the temperature operator and establishes the equivalence among constraint realizations. The approach naturally leads to thermodynamic uncertainty relations and suggests extensions to quantum and topological phase transitions, as well as black-hole and non-equilibrium thermodynamics.

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)
• Ergotropy-Based Quantum Thermodynamics [0.0]
  We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy.<n>As an application, the average heat can be used as a general non-Markovinity measure for unital maps.
  arXiv  Detail & Related papers  (2025-04-09T18:26:51Z)
• Unification of Stochastic and Quantum Thermodynamics in Scalar Field Theory via a Model with Brownian Thermostat [0.0]
  We present a systematic procedure to derive a quantum master equation for thermal relaxation in real scalar field theory.<n>We define heat, work, and entropy in a way that satisfies the first and second laws of quantum thermodynamics.
  arXiv  Detail & Related papers  (2025-03-04T23:48:29Z)
• Quantum Phase Space Approach to the Ideal Fermi and Bose Gases [0.0]
  improved models build upon the recently developed concepts of quantum phase space (QPS) and the QPS representation of quantum mechanics.<n>Work provides a foundation for further applications in nanoscale systems, quantum gases, low-temperature physics, ultracold physics, and astrophysics.
  arXiv  Detail & Related papers  (2024-07-13T20:45:41Z)
• Thermodynamics of adiabatic quantum pumping in quantum dots [50.24983453990065]
  We consider adiabatic quantum pumping through a resonant level model, a single-level quantum dot connected to two fermionic leads. We develop a self-contained thermodynamic description of this model accounting for the variation of the energy level of the dot and the tunnelling rates with the thermal baths.
  arXiv  Detail & Related papers  (2023-06-14T16:29:18Z)
• 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)
• 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)
• Geometric Quantum Thermodynamics [0.0]
  Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics. We develop both microcanonical and canonical ensembles, introducing continuous mixed states as distributions on the manifold of quantum states. We give both the First and Second Laws of Thermodynamics and Jarzynki's Fluctuation Theorem.
  arXiv  Detail & Related papers  (2020-08-19T21:55:25Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)
• 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.