{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:09:54Z","timestamp":1779376194304,"version":"3.53.1"},"reference-count":62,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Peter O\u2019Donnell Foundation","award":["#30212223"],"award-info":[{"award-number":["#30212223"]}]},{"name":"Jim Holland Foundation","award":["#30212279"],"award-info":[{"award-number":["#30212279"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Real-world autonomous agents learn under nonstationarity, safety constraints, and finite energetic budgets. We develop a framework for perennial learning\u2014agents that continuously refine their models while provably controlling the cost of forgetting\u2014by unifying three classical pillars: Kolmogorov complexity, which equates scientific discovery with algorithmic compression; Landauer\u2019s principle, which assigns a minimal thermodynamic cost of kBTln2 per erased bit to every irreversible model update; and port-Hamiltonian (PH) dynamics, whose (J\u2212R)\u2207H decomposition separates zero-cost reversible inference from costly irreversible forgetting by construction. The Maxwell demon analogy is formalized: each learning episode is a Szilard cycle in which information acquisition, belief transport, and memory erasure must balance thermodynamically. The information-distance framework, comprising the normalized information distance (NID) and normalized compression distance (NCD), provides a computable geometry for measuring learning progress and guiding curriculum design. We separate theideal uncomputable regularizer based on prefix complexity from the practical compressor\/MDL (minimum description length) surrogate that appears in optimization and prove a calibration lemma linking the two under a mild uniform-accuracy assumption. Under explicit regularity, compact-sublevel, and non-energy-extracting assumptions, we prove a passivity speed limit for curriculum-induced contractions of the effective feasible set. Under local asymptotic normality, we reprove that Fisher information is a local posterior codelength proxy rather than an exact theorem about algorithmic entropy. A conditional sequential information-budget proposition shows that the per-stage sample requirement scales as O\u02dc(\u0394kt\/\u03bb\u22c6), where \u0394kt is the number of materially changed model coordinates (not the total model complexity kt); the k3\u2192\u0394k improvement is conditional on a warm-start assumption and a chosen cold-start baseline. A double-integrator running example with a moving obstacle illustrates the architecture.<\/jats:p>","DOI":"10.3390\/e28050551","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:07:26Z","timestamp":1779206846000},"page":"551","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Physics, Information, and Computation of Perennial Learning: Kolmogorov Complexity, Information Distance, and Port-Hamiltonian Thermodynamics"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9619-3278","authenticated-orcid":false,"given":"Chandrajit","family":"Bajaj","sequence":"first","affiliation":[{"name":"Department of Computer Science and Oden Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1137\/S009753979324485X","article-title":"A new approach to formal language theory by Kolmogorov complexity","volume":"24","author":"Li","year":"1995","journal-title":"SIAM J. 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