Fractional Time Irreversibility Mathematical Physics Nonequilibrium Theory of Time

Mathematical analysis of time flow

R. Hilfer

Analysis 36, 49-64 (2016)

submitted on
Saturday, July 4, 2015

The mathematical analysis of time fow in physical many-body systems leads to the study of long-time limits. This article discusses the interdisciplinary problem of local stationarity, how stationary solutions can remain slowly time dependent after a long-time limit. A mathematical defnition of almost invariant and nearly indistinguishable states on C*-algebras is introduced using functions of bounded mean oscillation. Rescaling of time yields generalized time fows of almost invariant and macroscopically indistinguishable states, that are mathematically related to stable convolution semigroups and fractional calculus. The infnitesimal generator is a fractional derivative of order less than or equal to unity. Applications of the analysis are given to irreversibility and to a physical experiment.

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