Princeton University Press eBooks

Deductive Development of the Theory

John von Neumann

Published Feb 27, 2018• 0 citations

Abstract

This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ‎] (∥φ‎∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ‎] is the state φ‎).

DOI: 10.23943/princeton/9780691178561.003.0005

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