Thermodynamic origin of quantum time-energy uncertainty relation

• URL: http://arxiv.org/abs/2110.01337v1
• Date: Mon, 4 Oct 2021 11:34:51 GMT
• Title: Thermodynamic origin of quantum time-energy uncertainty relation
• Authors: Zacharias Roupas
• Abstract summary: Louis de Broglie tried to develop a theory of sub-quantum degrees of freedom relying on statistical thermodynamics. He realized a quantum particle as a fluctuating dense corpuscle formed via non-linear effects from a sub-quantum medium. We show here that, when the de Broglie temperature-time conjecture is assumed, the thermodynamic temperature-energy uncertainty relation leads to the quantum time-energy uncertainty relation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of time is a notable obstacle towards the recognition of quantum theory as the ultimate fundamental description of nature. Quantum theory may not be complete if founded upon classical notions. Louis de Broglie, seeming to be more or less convinced about the ontology of his proposed matter waves, tried to develop a theory of sub-quantum degrees of freedom relying on statistical thermodynamics. He realized a quantum particle as a fluctuating dense corpuscle formed via non-linear effects from a sub-quantum medium. A wave on the medium guides the vibrating corpuscle. He argued that an intrinsic clock of a quantum particle is related to its Brownian motion at the sub-quantum level. This led him to conjecture a relation between the de Broglie clock frequency $m c^2/h$ and its implicit temperature, which equals that of the surrounding sub-quantum medium. About the same time, Mandelbrot was the first to derive in a classical setting a thermodynamic uncertainty relation between energy and temperature, that was, coincidentally or not, anticipated by Bohr and Heisenberg in the first years of development of quantum theory. We show here that, when the de Broglie temperature-time conjecture is assumed, the thermodynamic temperature-energy uncertainty relation leads to the quantum time-energy uncertainty relation.

Related papers

• Proof of a Universal Speed Limit on Fast Scrambling in Quantum Systems [0.0]
  We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in nonequilibrium quantum dynamics.
  arXiv  Detail & Related papers  (2024-04-23T18:00:01Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Time-energy uncertainty relation in nonrelativistic quantum mechanics [0.0]
  The time-energy uncertainty relation in nonrelativistic quantum mechanics has been debated with regard to its formal derivation, validity, and physical meaning. We analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model. The presented results elucidate the fact that the time in the Schr"odinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.
  arXiv  Detail & Related papers  (2024-01-15T12:23:51Z)
• 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 dissipation and the virial theorem [22.1682776279474]
  We study the celebrated virial theorem for dissipative systems, both classical and quantum. The non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.
  arXiv  Detail & Related papers  (2023-02-23T13:28:11Z)
• Demonstrating Quantum Microscopic Reversibility Using Coherent States of Light [58.8645797643406]
  We propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit.
  arXiv  Detail & Related papers  (2022-05-26T00:25:29Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Irreversibility and the Arrow of Time [0.0]
  Irreversible behavior often manifests itself in the guise of entropy production. A derivation of the laws of thermodynamics from (quantum) statistical mechanics is presented. Results on diffusive (Brownian) motion of a quantum particle interacting with a quasi-free quantum-mechanical heat bath are reviewed.
  arXiv  Detail & Related papers  (2022-02-09T18:32:01Z)
• Taking the temperature of a pure quantum state [55.41644538483948]
  Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. We propose a scheme to measure the temperature of such pure states through quantum interference.
  arXiv  Detail & Related papers  (2021-03-30T18:18:37Z)
• Second quantization of time and energy in Relativistic Quantum Mechanics [0.0]
  canonical quantization of Special Relativity provides a unified origin for the existence of Dirac's Hamiltonian. Second quantization of the time operator field follows step by step that of the Dirac Hamiltonian field. An early connection is found allready in Feshbach's unified theory of nuclear reactions.
  arXiv  Detail & Related papers  (2021-02-01T18:24:50Z)

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.