{"paper":{"title":"Asymptotic hydrographs and anomalous dispersion in mass-conserving storage cascades","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.other","math.PR","physics.app-ph","physics.class-ph","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bal\\'azs S\\'andor, Henrique Santos Lima, M\\'ark Honti","submitted_at":"2026-06-19T04:52:02Z","abstract_excerpt":"Sums of independent exponential random variables lead to the Erlang distribution, providing a direct probabilistic route from exponential waiting times to the integer-shape gamma law. This paper investigates how this classical construction changes when the exponential waiting-time density is replaced by the $q$-exponential density of nonextensive statistics. Our main result is an analytical asymptotic expression for the outflow of a mass-conserving cascade of reservoirs driven by a $q$-exponential waiting-time kernel. In the critical case $q=5/3$, the large-cascade flow rate converges to a sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21095","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21095/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}