Informational Nostalgia: Memory Growth, the Irreducible Prediction Shortfall, and the Thermodynamics of Non-Stationary Learning

Actively held memory is not a record but a thermodynamic process that pays foritself. When a system holds a model of an environment that drifts faster than themodel is refreshed, a growing fraction of the stored bits no longer predictsanything — informational nostalgia — measured operationally by the predictionshortfall (the fraction of the environment's predictable future the systemmisses). The work extends the predictive efficiency of self-modeling to anon-stationary regime with growing memory, under a self-payment condition whosethermodynamic price is set by a separate Still bound. Two results are proved:Lemma 1 (holding a bit against thermodynamic erosion costs strictly positivepower, with an explicit lower bound) and Lemma 2 (a conditional result: under slowOrnstein-Uhlenbeck drift, any finite refresh rate, and a numerically verifiedadditivity assumption, the prediction shortfall asymptotically stays above anexplicit positive constant). Consequences: predictive capacity collapses above acritical nostalgia, and an optimal rate of complete memory reset exists; apre-registration-ready quantitative prediction is given for E. coli chemotaxis.This deposit contains: the manuscript (Russian primary and English translation, inMarkdown, LaTeX, and compiled PDF), supplementary material, bibliography, figures,and self-contained, seed-reproducible numerical experiments (drifting Markov chainsand a controlled continual-learning benchmark).Companion to "Vitality as the Efficiency of Self-Paid Self-Modeling"(A. Andriishin, 2026; https://doi.org/10.5281/zenodo.21039160).