Next Article in Journal
Quantum Entropy and Its Applications to Quantum Communication and Statistical Physics
Next Article in Special Issue
Principle of Minimum Discrimination Information and Replica Dynamics
Previous Article in Journal
Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions
Previous Article in Special Issue
Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics
Open AccessArticle

Entropy: The Markov Ordering Approach

1
Department of Mathematics, University of Leicester, Leicester, UK
2
Institute of Space and Information Technologies, Siberian Federal University, Krasnoyarsk, Russia
3
Department of Resource Economics, University of California, Berkeley, CA, USA
*
Author to whom correspondence should be addressed.
Entropy 2010, 12(5), 1145-1193; https://0-doi-org.brum.beds.ac.uk/10.3390/e12051145
Received: 1 March 2010 / Revised: 30 April 2010 / Accepted: 4 May 2010 / Published: 7 May 2010
(This article belongs to the Special Issue Entropy in Model Reduction)
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. View Full-Text
Keywords: Markov process; Lyapunov function; entropy functionals; attainable region; MaxEnt; inference Markov process; Lyapunov function; entropy functionals; attainable region; MaxEnt; inference
Show Figures

Graphical abstract

MDPI and ACS Style

Gorban, A.N.; Gorban, P.A.; Judge, G. Entropy: The Markov Ordering Approach. Entropy 2010, 12, 1145-1193.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Only visits after 24 November 2015 are recorded.
Search more from Scilit
 
Search
Back to TopTop