bibkey: jaynes1957information authors: E. T. Jaynes year: 1957 title: Information Theory and Statistical Mechanics doi: 10.1103/PhysRev.106.620 url: https://bayes.wustl.edu/etj/articles/theory.1.pdf claim: “For fixed finite alternatives and sufficient statistics, the normalized exponential law has log-partition derivatives equal to the corresponding expectations with the stated negative-exponent convention.” strata_touched: [] license: citation-only triage: anchor
Finite exponential-family comparison
The original article is in Physical Review 106, 620–630. The linked scanned reprint, printed p. 623, equations (2-9)–(2-12), gives the partition function, normalized exponential law and expectation derivative; equations (2-14)–(2-15) give fluctuation and parameter-response identities. The alternatives and sufficient statistics are fixed during differentiation.
The consumer is Static §24, Assumption 24.2. It substitutes the five Boolean states and the assigned statistic . The energy zero is additive gauge, and recovery of energy from a law fixes nonzero inverse temperature. A freely fitted positive five-state law is a saturated parametrization; this reference does not identify an observed occupation probability with physical energy or certify detailed balance.