dorsal/arxiv
View SchemaDifferential entropy and time
| Authors | Piotr Garbaczewski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408192 |
| URL | https://arxiv.org/abs/quant-ph/0408192 |
| DOI | 10.3390/e7040253 |
| Journal | Entropy 7: 253-299,2005 |
Abstract
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon) entropies is explained in case of non-equilibrium Smoluchowski processes. A very different temporal behavior of Gibbs and Kullback entropies is confronted. A specific conceptual niche is addressed, where quantum von Neumann, classical Kullback-Leibler and Gibbs entropies can be consistently introduced as information measures for the same physical system. If the dynamics of probability densities is driven by the Schr\"{o}dinger picture wave-packet evolution, Gibbs-type and related Fisher information functionals appear to quantify nontrivial power transfer processes in the mean. This observation is found to extend to classical dissipative processes and supports the view that the Shannon entropy dynamics provides an insight into physically relevant non-equilibrium phenomena, which are inaccessible in terms of the Kullback-Leibler entropy and typically ignored in the literature.
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"abstract": "We give a detailed analysis of the Gibbs-type entropy notion and its\ndynamical behavior in case of time-dependent continuous probability\ndistributions of varied origins: related to classical and quantum systems. The\npurpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon)\nentropies is explained in case of non-equilibrium Smoluchowski processes. A\nvery different temporal behavior of Gibbs and Kullback entropies is confronted.\nA specific conceptual niche is addressed, where quantum von Neumann, classical\nKullback-Leibler and Gibbs entropies can be consistently introduced as\ninformation measures for the same physical system. If the dynamics of\nprobability densities is driven by the Schr\\\"{o}dinger picture wave-packet\nevolution, Gibbs-type and related Fisher information functionals appear to\nquantify nontrivial power transfer processes in the mean. This observation is\nfound to extend to classical dissipative processes and supports the view that\nthe Shannon entropy dynamics provides an insight into physically relevant\nnon-equilibrium phenomena, which are inaccessible in terms of the\nKullback-Leibler entropy and typically ignored in the literature.",
"arxiv_id": "quant-ph/0408192",
"authors": [
"Piotr Garbaczewski"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th",
"physics.gen-ph"
],
"doi": "10.3390/e7040253",
"journal_ref": "Entropy 7: 253-299,2005",
"title": "Differential entropy and time",
"url": "https://arxiv.org/abs/quant-ph/0408192"
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