Physical entropy, information entropy and their evolution equations (Q1611731)

The author develops a theory of the dynamic information entropy and builds a nonlinear evolution equation of the information entropy density changing in time and density space. The mathematical form and physical meaning of this equation are similar to that of the physical entropy. The time rate of change of information entropy density originates from drift, diffusion and production. The concise statistical formula for this entropy is again similar to that of physical entropy. The paper also studies the similarity and differences between the two entropies and the possible unification of the two statistical entropies. It further discusses the relationship between the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy and their connection to the entropy evolution equation.