The Stochastic-Quantum Correspondence

• URL: http://arxiv.org/abs/2302.10778v2
• Date: Thu, 7 Sep 2023 02:41:01 GMT
• Title: The Stochastic-Quantum Correspondence
• Authors: Jacob A. Barandes
• Abstract summary: This paper introduces an exact correspondence between a general class of systems and quantum theory. This correspondence provides a new framework using Hilbert-space methods to formulate highly generic, non-Markovian types of dynamics. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the Hilbert-space, path-integral formulations, and quasiprobability formulations. In addition, this reconstruction approach opens up new ways of understanding quantum phenomena like interference, decoherence, entanglement, noncommutative observables, and wave-function collapse.

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