1 min read
| Status | Active — read 2026-10-20 (NOTE-975) in full, from the published version on Chorin's Berkeley page; worth reading for the exact generalized Langevin equation under three projections (conditional expectation, linear, finite-rank), for computing the memory kernel from equilibrium correlation functions through a Volterra equation, and for the t-damping (t-model) equation dΦ/dt = R̄(Φ) + tS(Φ) with its proof that, for separable Hamiltonians, it dissipates the effective energy (THEORY-752). Read it knowing that it has one 4-variable example, no error bound for any approximation, no Markovian augmentation by memory coordinates, that its abstract's "close to the best possible estimate" holds on that example only to t ≈ 8, and that the t-model it calls a short-memory approximation treats the kernel as constant over the whole window. |
| Version | 3 |
| Tags | mathematics, natural-sciences, probabilistic-modeling |
| Cited as “paper” by | NOTE-975 — Chorin, Hald and Kupferman — Optimal prediction with memory |
| Cited as “source” by | THEORY-752 — In optimal prediction of a Hamiltonian system with separable energy and canonical initial law, projected by conditional expectation, the t-model's leading-order memory term tPLQLx makes the effective Hamiltonian of the resolved variables non-increasing, so the eliminated variables' memory enters as a damping that grows linearly in time |
Chorin, A. J., Hald, O. H. & Kupferman, R. (2002). Optimal prediction with memory. Physica D 166(3–4): 239–257. doi:10.1016/S0167-2789(02)00446-3.
Read in full in NOTE-975. THEORY-752 is filed from it.
A5 called it “the most direct foundation for comparing reduced-model prediction, unresolved dynamics, and memory”, to be read before any reformulation of dynamical independence. Bears on QUESTION-222, THEORY-257 and CLAIM-327.