Dynamics, Thermodynamics, and Time-Asymmetry

Abstract

064 There are two schools, or lines of thought, that try to unify the apparently divergent laws of dynamics and thermodynamics and to explain the observed time-asymmetry of the universe, and most of its sub-systems, in spite of the fact that these systems are driven by time-symmetric evolution equations. They will be called the coarse-graining and the fine-graining schools (even if these names describe only a part of their philosophy). Coarse-graining school obtains time-asymmetry via a projection of the state space on a space of ''relevant'' states. The corresponding projection of the primitive reversible evolution laws yields effective irreversible evolution laws for the relevant states. Fine-graining always use the same primitive reversible evolution laws. But these laws (in adequate extensions of the usual spaces where these laws are formulated) have a set of solutions $S$ that can be decompose in two subsets $S_{+\text{}}$ and $S_{-}$ of time asymmetric solutions. Choosing one of these two sets, as the arena to formulate the theory, time asymmetry is established. The aim of these lectures is to explain, in the simplest- self-contained, unbiased, and, honest way, the main characteristics of both schools and to point out the advantages and disadvantages of both formalism, in such a way that, the polemic between the schools, turns out to be explicit and organized in the mind of the reader (who will be considered the supreme judge to give the final verdict). 064 Some cosmological features of the theory will be also considered, mainly the problem of the low entropy initial state of the universe