Specific heat anomalies of open quantum systems

G.-L. Ingold, P. Hänggi, and P. Talkner

Phys. Rev. E 79, 061105 (2009) DOI: 10.1103/PhysRevE.79.061105

The definition of the specific heat of an open damped quantum system is a subtle issue. A possible approach 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 in 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 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 effective partition function.

Casimir network (ESF) Supported by the ESF through the Casimir-Netzwerk.