Third order information measure describing a perturbed two-level system

Abstract

In this paper, we formulate a new measure of information measure that satisfies the validity conditions given by the Khinchin axioms. This new form of information measure is derived from the Hierarchy of information measures which is a differential equation of the form (d^n-1/dΦ^n-1)I_Φ^[n](pᵢ) = ∑^N_i=1 pᵢ^Φ ln(pᵢ) where we refer n as the order of information measure. Here, we will consider the third n=3 order information measure. The corresponding Statistical mechanics will be derived using Jaynes' Maximum Entropy Principle. The derived probability distribution will then be applied to a perturbed two-level system.