Abstract
It is shown that in the quantum theory of systems with a finite number of degrees of freedom which employs a set of algebraic states, a statistical element introduced by averaging the mean values of operators over the distribution of continuous quantities (a spectrum point of a canonical operator and time) is conserved for the limiting transition to the δ distribution. On that basis, quantum statistical dynamics, i.e., a theory in which dynamics (time evolution) includes a statistical element, is advanced. The theory is equivalent to orthodox quantum mechanics as regards the orthodox states, but is essentially different with respect to the coherence properties in a continuous spectrum. The measurement-process theory, including the statistical interpretation of quantum mechanics, and the irreversibility theory are constructed, and the law of increasing chaos, which is a strengthening of the law of entropy increase, is obtained. In our theory, mechanics and statistics are organically connected, whereby the fundamental nature of probabilities in quantum physics manifests itself.
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Mashkevich, V.S. Quantum statistical dynamics: Statistics origin, measurement, and irreversibility. Found Phys 15, 1–33 (1985). https://doi.org/10.1007/BF00738735
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DOI: https://doi.org/10.1007/BF00738735