Parametric invariance

• URL: http://arxiv.org/abs/2203.07262v1
• Date: Mon, 14 Mar 2022 16:41:46 GMT
• Title: Parametric invariance
• Authors: M\'ario J. de Oliveira
• Abstract summary: parametric invariance was used by Ehrenfest as a principle related to the quantization rules of the old quantum mechanics. We show that the slow parametric change leads to the adiabatic process, allowing the definition of entropy as a parametric invariance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We examine the development of the concept of parametric invariance in classical mechanics, quantum mechanics, statistical mechanics, and thermodynamics, and particularly its relation to entropy. The parametric invariance was used by Ehrenfest as a principle related to the quantization rules of the old quantum mechanics. It was also considered by Rayleigh in the determination of pressure caused by vibration, and the general approach we follow here is based on his. Specific calculation of invariants in classical and quantum mechanics are determined. The Hertz invariant, which is a volume in phase space, is extended to the case of a variable number of particles. We show that the slow parametric change leads to the adiabatic process, allowing the definition of entropy as a parametric invariance.

Related papers

• Relative state-counting for semiclassical black holes [0.0]
  entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. We construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states.
  arXiv  Detail & Related papers  (2024-04-24T18:00:01Z)
• Quantum simulation of the Fokker-Planck equation via Schrodingerization [33.76659022113328]
  This paper studies a quantum simulation technique for solving the Fokker-Planck equation. We employ the Schrodingerization method-it converts any linear partial and ordinary differential equation with non-Hermitian dynamics into systems of Schrodinger-type equations.
  arXiv  Detail & Related papers  (2024-04-21T08:53:27Z)
• Entanglement entropy in quantum black holes [2.3301643766310374]
  We discuss the entanglement entropy for a massive Klein-Gordon field in two Schwarzschild-like quantum black hole spacetimes. We estimate the free parameters for such quantum metrics through a simple physical argument based on Heisenberg uncertainty principle. Our findings reveal a significant decrease in entropy compared to the area law near the origin for the quantum metrics.
  arXiv  Detail & Related papers  (2024-03-31T15:19:03Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• Quantum stochastic thermodynamics: A semiclassical theory in phase space [0.0]
  A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space. We use a Fokker-Planck equation as the dynamics at the mesoscopic level. We define thermodynamic quantities based on the trajectories of the phase-space distribution.
  arXiv  Detail & Related papers  (2023-03-10T14:12:14Z)
• Quantum Mechanics From Principle of Least Observability [0.0]
  We show that the basic non-relativistic quantum formulations can be derived from a least observability principle. The principle extends the least action principle from classical mechanics by factoring in two assumptions.
  arXiv  Detail & Related papers  (2023-02-27T07:43:48Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Symmetry classification of typical quantum entanglement [10.698681396351494]
  Entanglement entropy of typical quantum states, also known as the Page curve, plays an important role in quantum many-body systems and quantum gravity. Our work elucidates the interplay of symmetry and entanglement in quantum physics and provides characterization of symmetry-enriched quantum chaos.
  arXiv  Detail & Related papers  (2023-01-18T20:41:32Z)
• 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)
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models [0.0]
  We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. We find that, in the thermodynamic limit, they have the same divergent behavior near the quantum phase transition. We also show that the scalar curvature is only defined on one of the system's phases and that it approaches a negative constant value.
  arXiv  Detail & Related papers  (2021-07-12T22:11:45Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)

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.