A Room, a Heater and a Window

Abstract

AbstractFirstly, we discuss the performances of the available approaches to non-equilibrium thermodynamics when it comes to describe the steady, stable configurations of a deceitfully simple system made of a room, a heater and a window: the linear non-equilibrium thermodynamics, Kirchhoff’s, Korteweg-Helmholtz’, Chandrasekhar’s, ‘maximum economy’ and ‘maximal entropy’ principle, Ziegler’s orthogonality principle, the constructal law, the ‘excess entropy production’ (with the related notion of ‘dissipative structure’), the ‘selective decay’ (which include Taylor’s and Turner’s principle in magnetohydrodynamics and extended magnetohydrodynamics, respectively), the ‘extended irreversible thermodynamics’, the ‘steepest ascent’, the ‘second entropy’, the ‘information thermodynamics’ (and the related ‘MaxEnt’), the ‘quasi-thermodynamic approach’ and the ‘entropy generation’ (related to Gouy-Stodola’s theorem). Secondly, we derive two necessary conditions of stability in systems at local thermodynamic equilibrium from Le Châtelier’s principle. Finally, we start from these two necessary conditions and retrieve all results listed above concerning stable steady states outside linear non-equilibrium thermodynamics as particular cases; moreover, we also retrieve Kohler’s principle for gases described by Boltzmann’s kinetic equation and the extremum properties of entropy production in both a radiation field, a radiating body, Liesegang rings in supersaturated solutions and gelation of polymers.