Combined Symmetry of Exponential and Extreme Hyperbolic Distributions in Macrosystems

Abstract

An extended entropy method has been developed that accounts for the finite properties of distributions and the stagewise character of relaxation processes. The kinetic properties of system agents (carriers and resources) determine the distribution type. If the time of relaxation of carriers is shorter, the exponential distribution is formed, whereas if the dynamic resources are more agile, an extreme heavy-tail hyperbolic distribution is formed. The exponential and extreme hyperbolic distributions have been found to possess combined symmetry, which is a different statistical interpretation of a single state.