The aim of this paper is to reconcile the two modes of description of macrosystems, i.e., to remove certain inconsistencies between the classical phenomenological and the quantum-theoretical descriptions of a macrosystem. Starting from Ludwig's formulation of a general framework for classical theories and his ansatz for a compatibility condition between the quantum theoretical and the classical mode of description for a macrosystem, we try to make clear what the “classical content” of many-body quantum theory really is. It is shown that (...) this classical content may be described by a certain “observable,” i.e., an operator-valued measure over the Borel sets of the classical trajectory space. There exists a reduced time evolution within this classical content which has the structure of a true semigroup in case of an irreversible classical time evolution. (shrink)

The physical implications of the embedding method recently proposed as the basic concept for a formulation of the general relationship between classical and quantum mechanical modes of description of macroscopic systems are further examined. A conceptual analysis of the idea of a macroobservable is given. A very general assumption on the macroobservables, called the thermodynamic uncertainty principle, leads then to a proposal for a formal reconstruction prescription for the macroobservables. The implications of this reconstruction method for the formal structure of (...) quantum statistical mechanics are discussed. (shrink)

The aim of the present paper is to show that the formalism of equilibrium quantum statistical mechanics can fully be incorporated into Ludwig's embedding scheme for classical theories in many-body quantum mechanics. A construction procedure based on a recently developed reconstruction procedure for the so-called macro-observable is presented which leads to the explicit determination of the set of classical ensembles compatible with the embedding scheme.

It is shown that the traditional formalism of equilibrium quantum statistical mechanics may fully be incorporated into a general macro-observable approach to quantum statistical mechanics recently proposed by the same author. (1,2) In particular, the partition functions which in the traditional approach are assumed to connect nonnormalized density operators with thermodynamic functions are reinterpreted as functions connecting so-called quantum mechanical effect operators with state parameters. It is argued that these functions although only part of a much richer internal structure of (...) the macro-observable are sufficient to cope with all problems one usually encounters in equilibrium quantum statistical mechanics. p]Denn eigentlich unternehmen wir umsonst, das Wesen eines Dinges auszudrücken. Wirkungen werden wir gewahr, und eine vollständige Geschichte dieser Wirkungen umfaßte wohl allenfalls das Wesen jenes Dinges.Johann W. v. Goethe Farbenlehre. (shrink)