Quantum statistical physics

Abstract

This chapter discusses the quantum statistical physics (QSP). It explains how QSP can claim to explain the collective properties of many-body systems: it postulates a quantum description at the microscopic level, while it has not obtained an ontological grasp of the individual components of these systems. The chapter discusses the Einstein's fluctuation formula and the particle-wave duality. The chapter also explains the extent to which the mathematics of classical ergodic theory may be generalized to the formalism of quantum theory; and the extent to which such generalizations may help formulate better certain aspects of the foundations of QSP. Boltzmann's works, most presentations of classical ergodic theory focus on the properties of the time-evolution––in particular on the transitivity of measures and the time-averages of observables. The chapter presents some of the evidences supporting the physical interpretation of the KMS condition proposed in as an alternative definition of equilibrium states in QSP.