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Quantum mechanics as kinetics

L. V. Prokhorov
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Abstract

Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic systems). The Planck constant and the Fock space appear after putting a dynamical system in a thermal bath. For harmonic oscillator in a thermal bath, the probability amplitudes can be identified with the complex valued phase functions $f(q+ip)$ describing small deviations from the equilibrium state, when the time of relaxation is large. A chain of such oscillators models both the one-dimensional space (or string), and one-dimensional quantum field theory.

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L. V. Prokhorov. 2005-03-25. Quantum mechanics as kinetics. https://arxiv.org/abs/quant-ph/0406079

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