  We investigate the basic theoretical issues in the quantum entanglement of
particle pairs created from the vacuum in a time-dependent background field or
spacetime. Similar to entropy generation from these processes which depends on
the choice of physical variables and how certain information is coarse-grained,
entanglement dynamics hinges on the choice of measurable quantities and how the
two parties are selected as well as the background dynamics of the field or
spacetime. We discuss the conditions of separability of quantum states in
particle creation processes and point out the differences in how the von
Neumann entropy is used as a measure of entropy generation versus for
entanglement dynamics. We show by an explicit construction that adoption of a
different set of physical variables yields a different entanglement entropy. As
an application of these theoretical considerations we show how the particle
number and the quantum phase enter the entanglement dynamics in cosmological
particle production.
