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 International Conference on Complex Systems (ICCS2007)

Maximal, Enforced, and Potential Entropy Production: towards an Understanding of Mechanisms for the Generation of Complexity

Daniel Polani
Adaptive Systems Research Group, School of Computer Science,

Philippe Capdepuy
Adaptive Systems Research Group, School of Computer Science, University of Hertfordshire

Chrystopher L. Nehaniv
Adaptive Systems Research Group, School of Computer Science, University of Hertfordshire

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     Last modified: November 28, 2007

The fundamental role of entropy in physics and its relation to the
informational state of an observer is well known, and finds its most
refined expression in the maximum entropy principle which relates the
most unbiased state of an only partly observed system to a description
of that very system in terms of thermodynamic equilibrium (e.g.
Jaynes, 1957b,a). Recently, there has been increased interest in
non-equilibrium systems which have been put forward for some time as
key to understand non-trivial dynamics as arising in complex and,
ultimately, living systems (Prigogine and Nicolis 1977). For a study
of stationary non-equilibrium systems, recent work has emphasized the
relevance of the Maximum Entropy Production Principle (Martyushev and
Seleznev 2006; Dewar 2005,2003), which revives a very related earlier
approach (Filyukov and Karpov 1967).

On the other side of the complexity spectrum, in recent work, we have
introduced empowerment, a quantity which is related (and sometimes
reduces to) the potential maximum entropy production which a
physically embedded, but energetically and informationally autonomous
agent can impinge on its environment (Klyubin et al. 2005a,b). There
are significant indications that this quantity could provide minimal
cognitive agents (see e.g. Beer, 1996; Swenson and Turvey, 1991) with
intrinsic drives towards ``interesting" and ``relevant" states in
the world, as also achieved by a number of methods based on different
principles (Kaplan and Oudeyer 2004; Der 2000; Steels 2004; Sporns and
Lungarella 2006; Prokopenko et al. 2006; Der et al. 1999).

In our work, we explore avenues to understand the relation between the
Maximum Entropy Production Principle and the dynamics imposed by the
empowerment principle (i.e. potential maximum entropy production) and
investigate the role that imposing enforced maximum entropy production
could play in such a context. The goal is to move towards bridging the
gap between comparatively simple (and ``passive") physical systems
and systems that seem to actively acquire increasingly higher levels
of organizations (such as would be required by intelligent, or living

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