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An attempt to unify statistical mechanics from the large deviation theoretical point of view is described. Theory of large deviations has already been applied to equilibrium statistical mechanics (mainly by mathematicians). However, nonequilibrium statistical physics (or statistical mechanics along the time axis) is a more interesting field to apply large deviation theory. From the large deviation point of view we can unify equilibrium statistical mechanics, statistical theory for chaos, for chaos, theory of multifractals, statistical theory for (non-equilibrium) steady states, and more. The point of view sheds light upon various foundational questions about nonequilibrium as well as equilibrium statistical physics. Although this paper contains expository parts for convenience and for the promotion of this point of view, the main aim is to explore a sound basis for nonequilibrium statistical physics.
Yoshitsugu Oono (Sun,) studied this question.