Entropies for coupled harmonic oscillators and temperature

We study two entropies of a system composed of two coupled harmonic oscillators which isbrought to a canonical thermal equilibrium with a heat-bath at temperature T . Using the purityfunction, we explicitly determine the Rényi and van Newmon entropies in terms of different physicalparameters. We will numerically analyze these two entropies under suitable conditions and showtheir relevance.

Keywords:

Two coupled harmonic oscillators , path integral , density matrix , thermal wavefunction , entropies