Statistical Thermodynamics of the Fr\"ohlich-Bose-Einstein Condensation of Magnons out of Equilibrium

TL;DR

This paper develops a non-equilibrium statistical thermodynamic framework to understand Fr"ohlich-Bose-Einstein condensation of magnons under radio-frequency pumping, revealing a complex two-fluid structure and stability criteria.

Contribution

It introduces a novel non-equilibrium thermodynamic approach to analyze magnon condensation, including entropy, fluctuations, and stability in dissipative systems.

Findings

Identification of a two-fluid model with normal and condensate components

Derivation of entropy production and fluctuation expressions in non-equilibrium

Verification of stability criteria using Glansdorff-Prigogine conditions

Abstract

A non-equilibrium statistical-thermodynamic approach to the study of a Fr\"ohlich-Bose-Einstein condensation of magnons under radio-frequency radiation pumping is presented. Such a system displays a complex behavior consisting in steady-state conditions to the emergence of a synergetic dissipative structure resembling the Bose-Einstein condensation of systems in equilibium. A kind of "two fluid model" arises: the "normal" non-equilibrium structure and Fr\"ohlich condensate or "non-equilibrium" one, which is shown to be an attractor to the system. We analyze some aspects of the irreversible thermodynamics of this dissipative complex system, namely, its informational entropy, expressions for the fluctuations in non-equilibrium conditions, the associated Maxwell relations and the formulation of a generalized $\mathscr{H}$-theorem. We also study the informational entropy production of the system, an order parameter is introduced and Glansdorff-Prigogine criteria for evolution and (in)stability are verified.