Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random Motion

Details Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random Motion Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random Motion

2005-04-05

arxiv.org/abs/cond-mat/0504115v1

Phys. Lett. A 341, (2005), 33-38

Physics

Condensed Matter

Statistical Mechanics

Subm. to Phys. Lett. A, full version available as quant-ph/0408192

Scientific paper

10.1016/j.physleta.2005.04.050

We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy "production" rate.

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