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A new theoretical approach to non-equilibrium statistical systems hasrecently been proposed by the author, a co-author and others. It is based on avariational principle which is associated with the discrepancy of a paththrough thermodynamical space to one following Liouvillean evolution. In thiscontribution the approach is extended in such a way that it can be applied to awide range of practical non-equilibrium statistical systems such as thosearising in turbulence but also to a general class of statistical physicsmodels. The new methodology allows for application to autonomous dynamicalsystems generalizing the previous work which applied only to Hamiltoniansystems. Furthermore it provides a general analysis of near equilibriumconditions which allows for a natural analysis of predictability limits inturbulent systems. Finally it describes a method is described for the numericalcalculation of far from equilibrium thermodynamical trajectories.

A non-equilibrium theoretical framework for statistical physics with application to turbulent systems and their predictability