Classical Statistics of Quantum Systems: Quantum State-Space Distributions and their Dynamics

The statistics of open quantum systems are determined by the interplay of classical uncertainty, describing the lack of knowledge of the initial preparation of the system and bath, and quantum uncertainty, originating from the wave-mechanical nature of quantum states. In this presentation, a classical probability distribution on quantum state space will be defined that separately encodes classical and quantum sources of uncertainty. The dynamics of such distributions will then be explored, revealing similar properties to Hamiltonian classical mechanics. In particular, the dynamics of closed systems is shown to be incompressible and time reversible, proving a quantum analog to the classical Liouville's theorem and framing quantum microreversibility equivalently to classical systems. This enables the application of tools from classical mechanics, statistical physics and fluid mechanics to quantum systems with applications in quantum information science and quantum thermodynamics.