Entropy Production in Stochastics
AbstractWhile 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
A printed edition of this Special Issue is available here.
Share & Cite This Article
Koutsoyiannis, D. Entropy Production in Stochastics. Entropy 2017, 19, 581.
Koutsoyiannis D. Entropy Production in Stochastics. Entropy. 2017; 19(11):581.Chicago/Turabian Style
Koutsoyiannis, Demetris. 2017. "Entropy Production in Stochastics." Entropy 19, no. 11: 581.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.