The Earth’s atmosphere is far from equilibrium; it is constantly in motion from the combined effects of gravity and planetary rotation, is constantly absorbing and emitting radiation, and hosts ongoing chemical reactions which are ultimately fuelled by solar photons. It has fluxes of material and energy across its boundaries with the planetary surface, both terrestrial and marine, and also emits a continual outward flux of infrared photons to space. The gaseous atmosphere is manifestly a kinetic system, meaning that its evolution must be described by time dependent differential equations. The equations doing this under the continuum fluid approximation are the Navier–Stokes equations, which are not analytically solvable and which support many non-linear instabilities. We have also seen that the generation of turbulence is a fundamentally difficult yet central feature of air motion, originating on the molecular scale. Non-equilibrium statistical mechanics may offer insight into which steady states a system far from equilibrium as a result of fluxes and anisotropies may migrate, without the need for detailed solution of the explicit path between the states. However, it does not seem possible to demonstrate mathematically that such steady states exist for the atmosphere. A physical view of the planet’s past and probable future suggests that the past and future evolution of the sun and its outgoing fluxes of energy may mean that the air-water-earth system may never have been or will ever be in a rigorously defined steady state. Also, to the human population, the detailed, time-dependent evolution is what matters in many respects. Nevertheless, non-equilibrium statistical mechanics is a discipline which should be applicable in principle to yield information about approximate steady states. These steady states may as a practical matter be definable from the observational record, for example the ice ages and the intervening periods evident in the geological record, or between states with two differing global average abundances of a radiatively active gas such as carbon dioxide. There has been great progress recently in non-equilibrium statistical mechanics, stemming from recent work on the concept of the maximization of entropy production.
Contributions to Statistical Mechanics Far from Equilibrium. III: Non-Perturbative Method for Steady States
