Irreversibility and Information in Mechanical Systems

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Abstract
Concepts from information theory are used to investigate the relation between measurement and irreversibility in finite, closed classical systems having known Hamiltonians. The effects of measurement upon the predictions of the observer are found for the cases of a single measurement, two simultaneous measurements, and two measurements at different times. The physical basis of coarse graining and the significance of the increase in the coarse‐grained entropy are discussed. An evolution equation is obtained describing the probability distribution of the measured quantities, and it is shown that this equation is non‐Markoffian. Despite this non‐Markoffian behavior, the distribution may behave irreversibly and may approach equilibrium. Thus, irreversible behavior is obtained without continual coarse graining. The condition for irreversible behavior is given for the case of a single measurement. The thermodynamic entropy is defined for general nonequilibrium situations.

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