An algebraic theory of infinite classical lattices III: Theory of single measurements

Details An algebraic theory of infinite classical lattices III: Theory of single measurements An algebraic theory of infinite classical lattices III: Theory of single measurements

2007-07-06

arxiv.org/abs/0707.0882v1

Physics

Mathematical Physics

9 pages, LaTex amsart

Scientific paper

This is the third in a series of papers dealing with the algebraic theory of infinite classical lattices. This paper presents a theory of single measurements on a lattice which we represent as comprising a finite subvolume--the system of measurement--immersed in an infinite surround or ``heat bath'' which determines the system's state. We consider the class of all stationary distributions on the set of microcanonical states of the infinite lattice. The theory addresses the question, ``For a lattice initially in state A, say, what is the probability that measurement of a certain quantity will take a value in (a,b)?'' Discussion includes description of the source of randomness in a measurement as well as characterization of the given states A.

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