Temperature-Induced Order in Quantum Many-Body Systems: Entropic Slaving

We provide an information-geometric framework that displays entropic slaving so as to characterize collective fermionic many-body features at finite temperatures. It posits that the statistical reorganization driving a many-body system toward highly correlated macroscopic configurations---such as fully Cooper-paired states---simultaneously restricts the statistical distinguishability of independent thermodynamic control parameters. This document details the mathematical formulation of this hypothesis utilizing the two-parameter Fisher information metric in a Lipkin-like SU2 model. In particular, it is shown that temperature can generate some kind of order in a quantum many body system. While the concept of entropic slaving has traditionally been confined to the phenomenology of complex biomolecular environments, we demonstrate that this behavior can indeed emerge as a fundamental property within closed quantum many-body systems stripped of biochemical specificity.