On the individual ergodic theorem on a logic
We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.
The hydrodynamic moment equations for a quantum system described by a two-band Hamiltonian are derived. In the case of pure states, it is proved that the order-0 and order-1 moment equations yield a closed system which is the two band analogue of Madelung's fluid equations.
In this paper, the authors introduce the notion of conditional expectation of an observable on a logic with respect to a sublogic, in a state , relative to an element of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.