The Perturbation Switched On from Forever: Kubo's Adiabatic Factor and the Preparation Inside Every Response Function
Year: 2026
Type: preprint
Abstract: In 1957 Ryogo Kubo made dissipation computable: his linear-response formulas express transport coefficients as equilibrium correlation functions of the unperturbed system, and that machinery — given its switching — is exact, and is the working instrument of transport theory. The derivation stands on a preparation no laboratory performs: the perturbation is applied adiabatically, with the factor e^{\epsilon t}, from t = -\infty, so that the unperturbed canonical ensemble is carried into the perturbed state, and \epsilon is sent to zero after the response is computed. This paper evaluates the switching at one declared address: a two-level system under a resonant drive, evolved exactly under six declared preparations, returns cycle-averaged responses spread over 0.182668 — sudden switching 0.588223, linear ramps 0.612442 and 0.705909, the adiabatic sequence itself 0.636460, 0.683201, 0.770890 at \epsilon = 0.500000, 0.250000, 0.125000, still moving by 0.087690 on its last declared step — while the formula reports the limit's single value. The value is transient-regime by construction and is printed as such; the dissipative steady state, the formula's own regime, is not contested. The formulas are the 1957 paper's derivations and stand entire. What is counted here is the derivation status of the preparation they stand on: 1 adiabatic-switching postulate, riding on the canonical ensemble counted at its own census address, 0 derivations in 1957 that physical preparations realize the limit. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.
Author: Aldred, William Alexander
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225390076