*John von Neumann*

*Nicholas A. Wheeler (ed.)*

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780691178561
- eISBN:
- 9781400889921
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691178561.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

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, ...
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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).Less

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).