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Entropy 2018, 20(11), 838; https://doi.org/10.3390/e20110838

Maximum Configuration Principle for Driven Systems with Arbitrary Driving

1,2
and
1,2,3,4,*
1
Section for the Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
2
Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
3
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
4
International Institute for Applied Systems Analysis, Schlossplatz 1, 2361 Laxenburg, Austria
*
Author to whom correspondence should be addressed.
Received: 11 September 2018 / Revised: 20 October 2018 / Accepted: 23 October 2018 / Published: 1 November 2018
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Abstract

Depending on context, the term entropy is used for a thermodynamic quantity, a measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in equilibrium or processes without memory, the mathematical expression for these different concepts of entropy appears to be the so-called Boltzmann–Gibbs–Shannon entropy, H. For processes with memory, such as driven- or self- reinforcing-processes, this is no longer true: the different entropy concepts lead to distinct functionals that generally differ from H. Here we focus on the maximum configuration entropy (that predicts empirical distribution functions) in the context of driven dissipative systems. We develop the corresponding framework and derive the entropy functional that describes the distribution of observable states as a function of the details of the driving process. We do this for sample space reducing (SSR) processes, which provide an analytically tractable model for driven dissipative systems with controllable driving. The fact that a consistent framework for a maximum configuration entropy exists for arbitrarily driven non-equilibrium systems opens the possibility of deriving a full statistical theory of driven dissipative systems of this kind. This provides us with the technical means needed to derive a thermodynamic theory of driven processes based on a statistical theory. We discuss the Legendre structure for driven systems. View Full-Text
Keywords: non-equilibrium; maximum configuration; maximum entropy principle; driven systems; statistical mechanics non-equilibrium; maximum configuration; maximum entropy principle; driven systems; statistical mechanics
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Hanel, R.; Thurner, S. Maximum Configuration Principle for Driven Systems with Arbitrary Driving. Entropy 2018, 20, 838.

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