The Emergence of Hydrodynamic Equations from Quantum Theory: A Decoherent Histories Analysis

Abstract

The most general description of the classical world is in terms of local densities(such as number, momentum, energy), and these typically evolve according toevolution equations of hydrodynamic form. To explain the emergent classicalityof these variables from an underlying quantum theory, it is therefore necessaryto show, first, that these variables exhibit negligible interference, and second,that the probabilities for their histories are peaked around hydrodynamic evolution.The implementation of this program in the context of the decoherent historiesapproach to quantum theory is described. It is argued that, for a system of weaklyinteracting particles, the eigenstates of local densities (averaged over a sufficientlylarge volume) remain approximate eigenstates under time evolution. This is aconsequence of their close connection with the corresponding exactly conserved(and so exactly decoherent) quantities. The subsequent derivation ofhydrodynamic equations from decoherent histories is discussed.