Thermodynamics of quantum heat bath (Q2832484)

Various quantum heat bath models have been utilized in physics, ranging back to the Calderia-Legget oscillator bath. In particular, an impact of the bath upon the (quantum) system coupled to it has been investigated in some depth; with the development of so-called information science, some simplifications of the general formalism proved to be necessary. Specifically, infinite-dimensional elementary systems (like, e.g., quantum gas molecules) are typically replaced by finite-dimensional ones. That refers not only to systems that are amenable to techniques of the general theory of open quantum systems (dissipative ones in this number), but also to the thermal bath models per se. In the present paper, the quantum bath models and their thermodynamics are based on the concept of weakly interacting ``molecules'', each having finitely many degrees of freedom (like, e.g., elementary two-level systems). Under some plausible assumptions it is demonstrated that the specific energy of the bath takes a canonical Gibbs-Boltzmann-looking form, involving expectation values of the Hamiltonian of the representative ``molecule'' with respect to admissible pure states. All results are obtained under an explicit input to the model which is a measure on the space of pure states of the ``molecule''. Candidates for such measure are analysed and a number of specific examples is discussed in the last section. The main result is an explicit formula for the specific entropy of the bath in the thermodynamic limit. Mathematical subtleties of the latter are bypassed and in fact its existence is assumed to be given a priori. The main advantage of that reasoning is that we illustrate how the microscopic features of ``molecular'' constituents determine the macroscopic properties of the bath.