This paper introduces HOpiPn, the higher-order pi-calculus with
_passivation_ and _name creation_, and develops an equivalence theory
for this calculus.  Passivation [Schmitt and Stefani] is a language
construct that elegantly models higher-order distributed behaviours
like failure, migration, or duplication (e.g. when a running process
or virtual machine is copied), and name creation consists in
generating a fresh name instead of hiding one.  Combined with
higher-order distribution, name creation leads to different semantics
from name hiding, and is closer to implementations of distributed
systems.  We define for this new calculus a theory of sound and
complete environmental bisimulation to prove reduction-closed barbed
equivalence and (a reasonable form of) congruence.  We furthermore
define environmental _simulations_ to prove behavioural
_approximation_, and use these theories to show non-trivial examples
of equivalence or approximation.  Those examples could not be proven
with previous theories, which were either unsound or incomplete under
the presence of process duplication and name restriction, or else
required universal quantification over general contexts.