On the origin of power-law distributions in systems with constrained phase space

Abstract

Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times, the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.