Classical stochastic approach to quantum mechanics and quantum thermodynamics

2023/09/04 by Mario J. de Olliveira, de Olliveira, Mario J. · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2309.01851

openalex publication_date 2023/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component ϕ_j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated to a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector which turns out to be of the Lindblad type. When the noise changes only the phase of ϕ_j, the Schrödinger and the quantum Liouville equation are obtained. The component ψ_j of the wave vector obeying the Schrödinger equation is related to stochastic wave vector by |ψ_j|²=⟨|ϕ_j|²⟩.

Cited by

• Boltzmann to Lindblad: Classical and Quantum Approaches to Out-of-Equilibrium Statistical Mechanics
• Stochastic interpretation of quantum mechanics

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