Out-of-equilibrium statistical physics of the Earth systemThe Earth and its various components (hydrosphere, atmosphere, biosphere, lithosphere) are typical out-of-equilibrium systems: due to the intrinsic dissipative nature of their processes, they are bound, without forcing, to decay to rest. However, in the presence of permanent forcing, a steady state regime can be established, in which forcing and dissipation equilibrate on average, allowing the maintenance of non-trivial steady states, with large fluctuations covering a wide range of scales. The number of degrees of freedom involved in the corresponding dynamics is so large that a statistical mechanics approach - allowing the emergence of global relevant quantities to describe the systems - would be welcome. Such a simplification would be especially welcome in the modeling of the fluid envelopes, where the capacity of present computers prohibits the full-scale numerical simulation of the (Navier-Stokes) equations describing them. Similar problems are ubiquitous in biology and environment, when the equations are known.
Another interesting outcome of a statistical approach would be to derive an equivalent of the Fluctuation-Dissipation Theorem (FDT), to offer a direct relation between the fluctuations and the response of the system to infinitesimal external forcing. Applied to the Earth system, such an approach could provide new estimates of the impact of climate perturbation through greenhouse gas emissions.
Various difficulties are associated with the definition of out-of-equilibrium statistical mechanics in the earth system, including:
- the problem of the definition of an entropy (possibly an infinite hierarchy of them) in heterogeneous systems;
- the identification of the constraints;
- the problem of the non-extensivity of the statistical variables, due to correlations between the different components of the system (possibly solved by introducing effective (fractional) dimensions).
On the physical side, several advances have been made recently in the description of turbulence, using tools borrowed from statistical mechanics for flows with symmetries. Variational principles of entropy production are also worth considering. Other advances have been made with regard to the equivalent of the FDT for physical systems far from equilibrium. Experimental tests in a glassy magnetic system have evidenced violation of the FDT through non-linearities in the relation between fluctuation and response. General identities between fluctuation and dissipation have been theoretically derived only for time-symmetric systems. They have been experimentally tested successfully in dissipative (non time-symmetric) systems like electrical circuits or turbulent flow. It would be interesting to extend these results to the Earth system.