A Note on Thermodynamics of the Harmonic Oscillator with Radiation Damping

Abstract

Previously one of the authors showed that the system with positive real impedance can be described within the framework of irreversible thermodynamics. In this paper we first remark that the impedance of the system which is describable by irreversible thermodynamics should necessarily be positive real. This conclusion is immediately drawn from the theorem of network synthesis that a system with non-positive-real impedance cannot be constructed from elementary RLC circuit. That a system is constructed from RLC circuit is the necessary and sufficient condition for the system to be described by irreversible thermodynamics. Then we examine some statistical properties of the harmonic oscillator with radiation damping, a typical example of the system with non-positive real impedance, which will help us to apprehend the above conclusion somewhat more intuitively. The main point is that in the presence of radiation damping, we cannot set up the Fokker-Planck equation for the fluctuation without having recourse to...