Semidefinite optimization as many-body thermodynamics: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks
Quantum thermodynamics unifies semidefinite programs (SDPs) in quantum information by mapping them to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. This framework interprets SDP objectives as system energies minimized via free energy functionals at a positive temperature T. It provides distinct statistical interpretations for states, measurements, and observables.