The Regression Hypothesis, Priced: What Onsager Assumed, What the Assumption Buys, and Where It Stops Being True
Year: 2026
Type: preprint
Abstract: Census pricing (row CC-91) of the regression hypothesis of Onsager's 'Reciprocal Relations in Irreversible Processes. I / II,' Phys. Rev. 37, 405 (1931); 38, 2265 (1931), member by member against a fixed bench (what is postulated, what is derived, what the notebook computes in a fully knowable test-bed, what it cannot reach). The reciprocal relations L_ij = L_ji are derived in the papers from assumed microscopic reversibility plus one stated statistical hypothesis -- that the regression of a spontaneous equilibrium fluctuation follows the same macroscopic law as the relaxation of a prepared state. Priced in linear Langevin dynamics, where the truth is known by construction: a prepared ensemble of 200,000 members relaxes on the macroscopic law 2e^(-lambda t) with worst deviation 0.0040, the spontaneous covariance matches the dynamics' own value (0.087204 against 0.087469), and the lagged correlation matrix is symmetric to the digits printed -- the hypothesis is a theorem of the assumed linear stochastic dynamics and its Gaussian equilibrium, neither derived in 1931. Entropy production is shown blind to the antisymmetric part of L (a non-reciprocal matrix returns the identical sigma = 20.220000), so the hypothesis carries the whole load; one step nonlinear, the stated law departs from the exact decay by 43.7-48.8%. Its 1950s linear-response justification keeps every fence and is credited to the later theory. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.
Author: Aldred, William Alexander
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225248216