On the entropy for unstable fermionic and bosonic states

We focus on the calculation of the entropy for decaying states in non-relativistic quantum mechanics. The starting point is the Friedrichs model in second quantization language. In this model, the Hamiltonian admits a spectral representation which includes resonances and Gamow states explicitly. In order to avoid the limitations posed by the definition of canonical probabilities in the presence of a complex spectrum, and/or the use of complex temperatures, we construct the partition function performing a path integration over coherent states. It is shown that the path integration yields results which are correct, at leading order, within the framework of the thermal perturbation theory. Finally, we obtain an expression for the canonical entropy of a quantum decaying system composed of fermion- and boson-states.