Category: Ergodicity

Categories
Ergodicity Fractional Time Irreversibility Statistical Physics Theory of Time

On Local Equilibrium and Ergodicity

R. Hilfer

Acta Physica Polonica B 49, 859 (2018)
DOI: 10.5506/APhysPolB.49.859

submitted on
Friday, April 27, 2018

The main mathematical argument of the universal framework for local equilibrium proposed in Analysis 36, 49 (2016) is condensed and formulated as a fundamental dichotomy between subsets of positive measure and subsets of zero measure in ergodic theory. The physical interpretation of the dichotomy in terms of local equilibria rests on the universality of time scale separation in an appropriate long-time limit.



For more information see

url

url
pdf

pdf
html

more
Categories
Ergodic Theory Ergodicity Fractional Time Mathematical Physics Theory of Time

Fractional Dynamics, Irreversibility and Ergodicity Breaking

R. Hilfer

Chaos, Solitons and Fractals 5, 1475 (1995)
https://doi.org/10.1016/0960-0779(95)00027-2

submitted on
Wednesday, September 28, 1994

Time flow in dynamical systems is analysed within the framework of ergodic theory from the perspective of a recent classification theory of phase transitions. Induced automorphisms are studied on subsets of measure zero. The induced transformations are found to be stable convolution semigroups rather than translation groups. This implies non-uniform flow of time, time irreversibility and ergodicity breaking. The induced semigroups are generated by fractional time derivatives. Stationary states with respect to fractional dynamics are dissipative in the sense that the measure of regions in phase space may decay algebraically with time although the measure is time transformation invariant.



For more information see

url

url
pdf

pdf
html

more