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Entropy: The Markov ordering approach

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journal contribution
posted on 2012-10-24, 09:08 authored by Alexander N. Gorban, P.A. Gorban, G. Judge
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.

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Citation

Entropy, 2010, 12 (5), pp. 1145-1193

Version

  • VoR (Version of Record)

Published in

Entropy

Publisher

MDPI, Basel, Switzerland.

eissn

1099-4300

Copyright date

2010

Available date

2012-10-24

Publisher version

http://www.mdpi.com/1099-4300/12/5/1145

Language

en

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