Algebraic Quantum Physics: Entropy & Entanglement
Abstract: In classical physics, the state of a system is a probability measure on functions on phase space. The latter commute. Classical physics is commutative probability theory. Quantum physics too can be described using states on an algebra, but the latter is non commutative : it is non- commutative probability theory. There is no need for a Hilbert space in this approach. Hilbert space then must be an emergent concept. We explain how this is so and show that unlike in classical physics, there are generically ambiguities in associating an entropy to a state in quantum theory. That is because there is in general no unique density matrix for a state. Transition from one such association to another is describable as a stochastic evolution with nondecreasing entropy. Remarkably this ambiguity is not there for Gibbs (KMS) states, a result of significance for phase transitions.
Reminder: Tea and cookies will be in the seminar room before the seminar.