It is clear that the total energy in a full gravitating $N$-body simulation should be conserved, but what about the energy of an individual particle? Is this not conserved, since the potential is itself time-dependent (due to interactions between particles)?
Alternatively, is the hamiltonian for a single particle in an $N$-body system conserved?
You're simulating reality. In real multi-body systems, a particle can get a gravity boost, even to the point where it reaches escape velocity and gets kicked out of the system (or the "system" involves a particle that's not gravitationally bound). By the same token, a particle can get a gravity brake and fall inward toward the barycenter.
So -- yes, energy can be exchanged between particles.
