Confirmed
So Okada
Title: Merged-log-concavity of rational functions and phase transitions of ideal boson and fermion gases
Abstract:
We introduce and discuss the merged-log-concavity of rational functions. It extends
q-exponentials (quantum dilogarithms) to some extent by polynomials with positive
integer coefficients and almost strictly unimodal sequences. Loosely speaking, it
extends Stanley's q-log-concavity of polynomials. Also, we discuss
phase transitions of ideal boson and fermion gases by the mathematical
theory of the merged-log-concavity. In particular, we consider vacua
of lowest
Helmholtz free energies. By the phase transitions, zero particle vacua
become non-zero particle vacua as temperature rises.