Thermodynamic anomalies in the presence of dissipation: from the free particle to the harmonic oscillator

Abstract

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat or reentrant classicality. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator's energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.

10 pages, 5 figures

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• Control of quantum thermodynamic behaviour of a charged magneto oscillator with momentum dissipation
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• Damped oscillators within the general theory of Casimir and van der Waals forces
• Anomalies in the specific heat of a free damped particle: The role of the cutoff in the spectral density of the coupling
• Path-integral approach to the thermodynamics of bosons with memory: Density and correlation functions