We show that for a large class of stationary Markov processes the total variation distance between the final equilibrium distribution and that at a given time is a strongly monotonic vanishing function. We illustrate this for basic paradigmatic processes and discuss how, for systems susceptible to a canonical description, this can be interpreted as a statistical arrow of time that exists besides the standard decrease of free energy.
Intrinsic irreversibility of Markovian chains / P., Di Porto; B., Crosignani; DEL RE, Eugenio. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - ELETTRONICO. - 89:5(2014), pp. 052118-1-052118-6. [10.1103/physreve.89.052118]
Intrinsic irreversibility of Markovian chains
DEL RE, EUGENIO
2014
Abstract
We show that for a large class of stationary Markov processes the total variation distance between the final equilibrium distribution and that at a given time is a strongly monotonic vanishing function. We illustrate this for basic paradigmatic processes and discuss how, for systems susceptible to a canonical description, this can be interpreted as a statistical arrow of time that exists besides the standard decrease of free energy.| File | Dimensione | Formato | |
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PhysRevE.89.052118.pdf
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