| In thermodynamics, as in classical mechanics, observables come in conjugate pairs: pressure/volume, temperature/energy etc. The mathematical formalism is quite different though, because the thermodynamic phase space is always odd-dimensional. We will show that in the quantum theory, this leads to a new thermodynamic uncertainty principle. Observables are described by operators, and the state of the system by a complex valued function of the extensive variables. Some applications to superconductors and superfluids will be outlined. There may also be connections to the quantum mechanics of blackholes. |