Thermodynamic free-energy spectrum theory for open quantum systems

In this work, we develop the free-energy spectrum theory for thermodynamics of open quantum impurity systems that can be either fermionic or bosonic or combined. We identify two types of thermodynamic free-energy spectral functions for open quantum systems and further consider the thermodynamic limit, which supports the Gaussian-Wick description of hybrid environments. We can then relate the thermodynamic spectral functions to the local impurity properties. These could be experimentally measurable quantities, especially for the cases of quantum dots embedded in solid surfaces. Another type of input is the bare-bath coupling spectral densities, which could be accurately determined with various methods. For illustration, we consider the simplest noninteracting systems, with focus on the strikingly different characteristics between the bosonic and fermionic scenarios.