Specific heat anomalies of open quantum systems

TL;DR

This paper investigates the peculiar behavior of specific heat in open quantum systems, revealing conditions under which the specific heat difference can be negative or show anomalies, and discusses implications for thermodynamics and density of states interpretation.

Contribution

It provides a detailed analysis of specific heat anomalies in open quantum systems, clarifying the interpretation of negative or dip-like behaviors and their thermodynamic consistency.

Findings

Specific heat difference can be negative in damped quantum systems.

Dips in specific heat difference occur under certain conditions for harmonic oscillators.

Minimal models help explain anomalous temperature dependence of specific heat.

Abstract

The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being an open system this quantity then naturally must be interpreted as the change of the specific heat obtained as the difference between the specific heat of the heat bath coupled to the system degrees of freedom and the specific heat of the bath alone. While this difference may become negative, the involved specific heats themselves are always positive; thus, the known thermodynamic stability criteria are perfectly guaranteed. For a damped quantum harmonic oscillator, instead of negative values, under appropriate conditions one can observe a dip in the difference of specific heats as a function of temperature. Stylized minimal models containing a single oscillator heat bath are employed to elucidate the occurrence of the anomalous temperature dependence of the corresponding specific heat values. Moreover, we comment on the consequences for the interpretation of the density of states based on the thermal partitionfunction.