Quantum mechanics for classical transport equations

Abstract:Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function. Its unitary evolution obeys a Schrödinger equation. Statistical observables measure properties of the classical probability distribution. In the quantum formalism they are represented by operators which do not commute with the ones associated to classical observables. Momentum, quantum energy and angular momentum or charges yield conserved quantities which constrain the evolution of the classical probability distribution. The characteristic features of quantum mechanics, as the superposition of wave functions, interference, the importance of phases, non-commuting operators or a unitary time evolution, are realized by probabilistic classical transport equations. Stochastic transport equations are described by a quantum system with a stochastic Hamiltonian.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Cellular Automata and Lattice Gases (nlin.CG)

arXiv:2605.15969 [quant-ph]

(or arXiv:2605.15969v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.15969 Focus to learn more arXiv-issued DOI via DataCite

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