  We extend the notion of conservativeness, given by Fredkin and Toffoli in
1982, to generic gates whose input and output lines may assume a finite number
d of truth values. A physical interpretation of conservativeness in terms of
conservation of the energy associated to the data used during the computation
is given. Moreover, we define conservative computations, and we show that they
naturally induce a new NP-complete decision problem. Finally, we present a
framework that can be used to explicit the movement of energy occurring during
a computation, and we provide a quantum implementation of the primitives of
such framework using creation and annihilation operators on the Hilbert space
C^d, where d is the number of energy levels considered in the framework.
