Reductions in dynamical theories

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Abstract
Can dynamical equations arising in nonequilibrium statistical mechanics be formulated in such a way that they become manifestly compatible with other, more macroscopic, dynamical theories? We show that the bracket formulation introduced previously answers the question if the more macroscopic theory is equilibrium thermodynamics. An extension of the bracket formulation, called a dynamic bracket formulation, is introduced in this paper. It provides an answer to the question also if the more macroscopic theories are dynamical theories. The dynamical bracket formulation reveals also a thermodynamics‐like structure that is naturally associated with more macroscopic dynamical theories.