Distinction of classical convex structures in the general framework of statistical models.

*(English)*Zbl 0774.46042
Measure theory, Proc. 2nd Winter Sch., Liptovský Ján/Czech. 1990, 79-84 (1990).

Summary: [For the entire collection see Zbl 0725.00004.]

The general framework of statistical models considered here has been developed on the basis of the operational approach to quantum theory and to statistical theories in general. For the roots of this approach G. Ludwig, E. B. Davies and J. T. Lewis, A. Holevo shall be quoted, but there are many other authors who followed this trend up to now. In this general scheme the problem to distinguish between classical and quantal models can be settled in different manners. In the following we propose a formulation which seems to us very simple and appropriate to modern formulations of statistical models.

The general framework of statistical models considered here has been developed on the basis of the operational approach to quantum theory and to statistical theories in general. For the roots of this approach G. Ludwig, E. B. Davies and J. T. Lewis, A. Holevo shall be quoted, but there are many other authors who followed this trend up to now. In this general scheme the problem to distinguish between classical and quantal models can be settled in different manners. In the following we propose a formulation which seems to us very simple and appropriate to modern formulations of statistical models.

##### MSC:

46N50 | Applications of functional analysis in quantum physics |

82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |

82B10 | Quantum equilibrium statistical mechanics (general) |