Dynamics, Thermodynamics, and Time Asymmetry

There are two schools, or lines, of thoughtwhich attempt to unify the apparently divergent laws ofdynamics and thermodynamics and to explain the observedtime asymmetry of the universe and most of its subsystems in spite of the fact that thesesystems are driven by time-symmetric evolutionequations. They will be called the coarse-graining andthe extended dynamics schools (even if these names onlypartially describe their philosophy). The coarse-grainingschool obtains time asymmetry via a projection of thestate space onto a space of relevantstates. The corresponding projection of the primitivereversible evolution laws yields effective irreversibleevolution laws for the relevant states. Extendeddynamics always uses the same primitive reversibleevolution laws. But these laws (in adequate extensionsof the usual spaces where they are formulated)have a set of solutions S that can be decomposed intotwo subsets S₊ and S_- oftime-asymmetric solutions. Time asymmetry is establishedby choosing one of these two sets as the arena in which to formulate thetheory. This paper explains in the simplestself-contained and unbiased way the main characteristicsof both schools and points out the advantages anddisadvantages of each, in such a way as to make explicit thedebate between the schools. Some cosmological featuresof the theory are also considered, mainly the problem ofthe low-entropy initial state of the universe.