Nonequilibrium statistical information theory

Abstract

In t his paper, we propose a nonequilibrium statistical information theory, whose ke rnel is information(entropy) evolution equation describing information evolution law. A nonlinear evolution equation of Shannon information (entropy) is derived . The statistical physical information is introduced and its nonlinear evolution equation is derived. Both of these two information (entropy) evolution equatio ns show that the temporal change rate of statistical information (entropy) densi t y originates together from their drift, diffusion and dissipation (production) i n coodinate space (and state variable space). The expressions of drift informati on flow and diffusion information flow, the concise formulas of statistical entr opy production rate and statistical information dissipation are given. The stati stical information dissipation (or increase) rate being equal to its statistical entropy production (or decrease) rate of the dynamic system, the information di ffusion and information dissipation occuring at the same time are proved. The d ynamic mutual information and dynamic channel capacity reflecting the dynamic di ssipative character in transmission process is presented. The similarities and dissimilarities between Shannon information (entropy),its evolution equation an d physical information (entropy),its evolution equation are discussed.