Dissipative evolution, initial conditions, and information theory

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Abstract
An information-theoretic approach is used to give a straightforward procedure that allows one to determine whether dissipative behavior can be attained for a given Hamiltonian. This technique stresses the importance of an adequate set of initial conditions in order to obtain dissipative evolution. It is shown that, although dissipative solutions may be compatible with the set of dynamical equations, they may not be realized just because it is impossible to construct the adequate set of initial conditions that would result in dissipative behavior. This is illustrated by reference to the well-known Bateman generalized problem of two interacting harmonic oscillators. We demonstrate the impossibility of obtaining dissipative evolution in linear, time-independent Hamiltonian systems generated with any combination of bilinear products of creation and annihilation operators.