Escort distribution, energy, and relative entropy of macrosystems with nonlinear pair interactions

Abstract

This paper is devoted to priority directions [1–3] of replicator dynamics, namely, to the study of models of macrosystems with nonlinear pair interactions. Let p(t) = (p1(t), p2(t), …, pn(t)) denote the column vector in which pi(t) is the relative number (concentration) of objects of type i in the macrosystem at a moment t. By e = (1, …, 1) we denote the unit column vector and by e T , the unit row vector. In this notation, p(t) ∈ = {p ∈ n : p i ≥ 0, i =1 ,,, n, e T p = 1}, where is the