Abstract
Entropy of a quantum oscillator in the presence of a quantum environment (or heat bath) is studied here. The spectral density, which comprises the environmental influences, here corresponds to a quasi-monochromatic thermal harmonic noise.
This further implies that the environment is a structured one compared to the usually employed unstructured strictly ohmic environment. The entropy is found to be vanishing as the temperature approaches its absolute zero value, which thereby guarantees the third law of thermodynamics.
At very high temperatures the classical behavior is observed. Similar to the usually employed ohmic-Drude bath model, the coefficient of the leading temperature dependent term in the entropy (at low temperatures) is proportional to the damping strength but not on other parameters of the spectral density characterising the bath.