On the power-law q-distribution function based on the probabilistically independent postulate in nonextensive statistics

TL;DR

This paper revises the power-law q-distribution in nonextensive statistics to align with the probabilistically independent postulate, enabling it to describe nonequilibrium stationary states in many-body systems with nonextensive energy.

Contribution

It introduces a new form of the power-law q-distribution consistent with the probabilistically independent postulate, extending its applicability to nonequilibrium stationary states.

Findings

The usual q-distribution may not satisfy the probabilistically independent postulate.

The proposed q-distribution can describe nonequilibrium stationary states.

The new distribution accounts for nonextensive energy in many-body systems.

Abstract

We deal with the power-law q-distribution functions, so-called q-exponentials in nonextensive statistics. The system considered is a many-body Hamiltonian system with arbitrary interacting potentials. We find that the usual form of power-law q-distribution function employed in nonextensive statistics for the system may be not to stand by the probabilistically independent postulate and it only represents a dynamical isothermal situation. The probabilistically independent postulate is validated by the nonextensivity (or pseudoadditivity) in nonextensive statistics and thus the usual forms of power-law q-distribution function have to be modified. In this letter, we present a new power-law q-distribution based on the probabilistically independent postulate, which can represent nonequilibrium stationary state of the system away from equilibrium and with the nonextensive energy.