Global non-equilibrium thermodynamics of stationary states applied to the Rayleigh-Bénard convection

Abstract: Classical thermodynamics describes physical systems in thermodynamic equilibrium, characterized in particular by the absence of macroscopic motion. Global non-equilibrium thermodynamics extends this framework to include physical systems in stationary states (Ho{\l}yst et al., EPL 149, 30001 (2025)). Here, we demonstrate that this extended theory captures macroscopic motion in stationary states, thereby providing a unified framework for global thermodynamics and fluid mechanics. We apply the theory to stationary Rayleigh-B\'enard convection and show how the second law of global non-equilibrium thermodynamics determines the direction of changes in fluid motion.