bibkey: gouasmiparishduraisamy2017memory authors: Ayoub Gouasmi; Eric J. Parish; Karthik Duraisamy year: 2017 title: A priori estimation of memory effects in coarse-grained nonlinear systems using the Mori–Zwanzig formalism doi: 10.1098/rspa.2017.0385 url: https://arxiv.org/abs/1611.06277 claim: Section 2.1 equations (2.1)–(2.3) separate instantaneous dynamics, the hidden-initial-state term and the convolution memory term of a finite block linear system. strata_touched: [] license: citation-only triage: anchor

Linear elimination and memory

Proceedings of the Royal Society A 473, article 20170385. The arXiv record identifies the authors and journal DOI. In arXiv:1611.06277v2, §2.1, equations (2.1)–(2.3), the hidden linear block is solved by variation of constants and substituted into the resolved equation. The discussion immediately after (2.3) distinguishes the three terms and explicitly notes that this exact rewriting is not a reduced-order model on cost grounds. The introductory example subsequently takes zero hidden initial data; that specialization does not remove the initial term in the general formula.

The FIB boundary geometry volume §18 uses blocks (-A,-B,-Bᵀ,-D) and keeps arbitrary hidden initial data. Its discrete memory input in §33 is already present in the observer-relative spacetime volume §19.2. Vanishing feedback kernels, decay estimates and autonomous compressed evolution have different hypotheses; the continuous paper is not an assertion of unconditional discrete stability or cheaper computation.