Damped oscillators within the general theory of Casimir and van der Waals forces

It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible frequency and temperature dependent dissipative susceptibilities of the heat bath constituents, influenced by the additional dissipative environmental channels that are not directly linked to the system oscillator. Consequently, the results obtained are applicable to the frequency and temperature dependent damping function of the system oscillator.