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 to evolution equations of hydrodynamic form. To explain the emergent classicality of these variables from an underlying quantum theory, it is therefore necessary to show, firstly, that these variables exhibit negligible interference, and secondly, that the probabilities for histories of them are peaked around hydrodynamic evolution. The implementation of this programme in the context of the decoherent histories approach to quantum theory is described. It is argued that, for a system of weakly interacting particles, the eigenstates of local densities (averaged over a sufficiently large volume) remain approximate eigenstates under time evolution. This is a consequence of their close connection with the corresponding exactly conserved (and so exactly decoherent) quantities. The subsequent derivation of hydrodynamic equations from decoherent histories is discussed.