Harmonic Oscillator, Dissipation, and Thermodynamics

Abstract A loss-free harmonic oscillator when treated as the working substance in a cylinder with a piston exhibits dissipation characterized by hysteresis cycles. Dissipation in this case develops through conversion of potential energy of the springs and part of the work by piston motion to kinetic energy of the oscillator that represents its temperature. The results also yield analogies with several complex thermodynamic notions such as lost work, heating and cooling, Joule–Thompson expansion and temperature inversion, and regimes of maximum power and maximum efficiency as in finite thermodynamic systems. Use of multiple oscillators with different frequency distributions supports the notion of a dissipative constitutive relationship emerging from a dissipation-free model in which the stress depends on both strain and strain rates as in heuristic models used in solid mechanics as, for example, the Johnson-Cook model.