nucleation

LIT-1882: Correspondence between thermodynamics and inference

1 min read

Properties5
StatusActive — read 2026-10-31 (NOTE-1481; appendices B, C1, C3, C4 skimmed); worth reading as the fullest working of the evidence-as-partition-function dictionary with sample size as inverse temperature: generalization error as equipartition, a "learning capacity" equal to K/2 in regular and to the RLCT in singular models (THEORY-1253), and a sample-size-dependent prior that reproduces AIC. The dictionary is formal; it has no physical currents or dissipation.
Version2
Tagsmathematical-statistics, model-comparison, thermodynamics, anthology-candidate
Cited as “paper” byNOTE-1481 — LaMont & Wiggins — thermodynamics and inference
Cited as “source” byTHEORY-1253 — Treating the Bayesian evidence as a partition function with sample size as inverse temperature, the analogue of heat capacity, the rate at which leave-one-out predictive loss falls with sample size, equals half the parameter count in a regular model, as equipartition, and the real log canonical threshold in a singular one, falling below these where prior or discreteness fixes parameters; with multiplicity above one the approach to the singular value is only logarithmic, and the correspondence has no counterpart of physical current or dissipation

Graph View

LaMont, C. H., & Wiggins, P. A. (2019). Correspondence between thermodynamics and inference. Physical Review E, 99, 052140.

Read in NOTE-1481.

Why this is here

A14’s starting point for setting SLT’s e^{-nK} beside a physical e^{-ΩV}. A14 itself kept them apart: the same statistical geometry does not fix the same physical currents or dissipation. Bears on THEORY-087. The reading bears A14’s caution out. The paper’s temperature is a sample size, and its dictionary has no dynamics, so nothing in it corresponds to a current, a housekeeping dissipation or an escape path, which are what LIT-1892 and LIT-1881 attach to maintained physical states. What it does give THEORY-087 is a second derivative of the Occam penalty with an equipartition reading (THEORY-1253). That derivative approaches the RLCT only logarithmically when the multiplicity exceeds one, as in CASE-152’s model.

Backlinks