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Interactive statistical mechanics and nonlinear filtering

Newton, NJ (2008) 'Interactive statistical mechanics and nonlinear filtering.' Journal of Statistical Physics, 133 (4). 711 - 737. ISSN 0022-4715

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Abstract

This paper connects non-equilibrium statistical mechanics and optimal nonlinear filtering. The latter concerns the observation-conditional behaviour of Markov signal processes, and thus provides a tool for investigating statistical mechanics with partial observations. These allow entropy reduction, illustrating Landauer's Principle in a quantitative way. The joint process comprising a signal and its nonlinear filter is irreversible in its invariant distribution, which therefore corresponds to a non-equilibrium stationary state of the associated joint system. Macroscopic entropy and energy flows are identified for this state. Since these are driven by observations internal to the system, they do not cause entropy increase, and so the joint system makes statistical mechanical sense in reverse time. Time reversal yields a dual system in which the signal and filter exchange roles. Despite the structural similarity of the original and dual systems, there is a substantial asymmetry in their complexities. This reveals the direction of time, despite the systems being in stationary states that do not produce entropy. © 2008 Springer Science+Business Media, LLC.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 05 Mar 2013 16:21
Last Modified: 17 Aug 2017 18:02
URI: http://repository.essex.ac.uk/id/eprint/5536

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