Classical stochastic approach to quantum mechanics and quantum thermodynamics

• URL: http://arxiv.org/abs/2309.01851v1
• Date: Mon, 4 Sep 2023 22:47:22 GMT
• Title: Classical stochastic approach to quantum mechanics and quantum thermodynamics
• Authors: Mario J. de Olliveira
• Abstract summary: 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 $phi_j$ of the wave vector is understood as a 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\phi_j$ 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 $\phi_j$, the Schr\"odinger and the quantum Liouville equation are obtained. The component $\psi_j$ of the wave vector obeying the Schr\"odinger equation is related to stochastic wave vector by $|\psi_j|^2=\langle|\phi_j|^2\rangle$.

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