Quasilocal energy conditions

The classical value of the Hamiltonian for a system with timelike boundary has been interpreted as a quasilocal energy. This quasilocal energy is not positive definite. However, we derive a `quasilocal dominant energy condition' which is the natural consequence of the local dominant energy condition. We discuss some implications of this quasilocal energy condition. In particular, we find that it implies a `quasilocal weak energy condition'.