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Entropy 2017, 19(11), 581; https://doi.org/10.3390/e19110581

Entropy Production in Stochastics

Department of Water Resources, School of Civil Engineeringh, National Technical University of Athens, 15780 Athina, Greece
Received: 14 September 2017 / Revised: 21 October 2017 / Accepted: 23 October 2017 / Published: 30 October 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
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Abstract

While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT) or conditionally on the past and present having been observed (CEPLT). We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed. View Full-Text
Keywords: entropy production; conditional entropy production; stochastic processes; scaling; climacogram; turbulence entropy production; conditional entropy production; stochastic processes; scaling; climacogram; turbulence
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Koutsoyiannis, D. Entropy Production in Stochastics. Entropy 2017, 19, 581.

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