section_path: Theoretical foundation/Generalized temperature from single-particle statistics
section_name: Generalized temperature from single-particle statistics
paragraph_text: Generalized temperature from single-particle statistics
  
  It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space ensembles given in statistical mechanics in the case of thermal and particle exchange between a small system of fermions (N even less than 10) with a single/double-occupancy system. The finite quantum grand canonical ensemble, obtained under the hypothesis of ergodicity and orthodicity, allows expressing the generalized temperature from the ratio of the average time of occupation τ 1 {\displaystyle \tau _{1}} and τ 2 {\displaystyle \tau _{2}} of the single/double-occupancy system:
  
  where E is the Fermi energy. This generalized temperature tends to the ordinary temperature when N goes to infinity.