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Maximum entropy principle and Landau free energy inequality
Authors: Bebiano, N; da Providencia, J
Ref.: Linear Multilinear Algebra 69(6), 1020-1034 (2021)
Abstract: In this paper, the following problem is considered: given two Hermitian matrices H and K and two real numbers x and y, determine a positive semidefinite matrix ρ such that the von Neumann entropy −Trρlogρ is maximum, subject to the condition that TrρH=x and TrρK=y. This question arises in information theory and in statistical mechanics in connection with the maximum-entropy inference principle. To answer it, we use this principle and numerical range methods.
