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While Physics-Informed Neural Networks (PINNs) successfully solve differential equations, current architectures remain inherently domain-specific. The extraction of domain-invariant entropy representations across fundamentally different physical laws remains unexplored. This paper introduces a unified Physics-Informed Deep Learning (PIDL) framework that simultaneously enforces differential equation residuals and information-theoretic bounds within a single neural architecture. We demonstrate this framework via two canonical studies: (i) a thermodynamic continuous stirred-tank reactor (CSTR) model solving governing ODEs, where a Softplus constraint strictly enforces the Second Law of Thermodynamics; and (ii) an information-theoretic financial market model solving the inverse Fokker-Planck PDE to infer latent drift and diffusion","title":"Physics-Informed Deep Learning for Entropy Prediction in Heterogeneous Systems: Thermodynamic and Information-Theoretic Case Studies","url":"https://arxiv.org/abs/2606.01179","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.01179v1 Announce Type: cross \nAbstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems. While Physics-Informed Neural Networks (PINNs) successfully solve differential equations, current architectures remain inherently domain-specific. The extraction of domain-invariant entropy representations across fundamentally different physical laws remains unexplored. This paper introduces a unified Physics-Informed Deep Learning (PIDL) framework that simultaneously enforces differential equation residuals and information-theoretic bounds within a single neural architecture. We demonstrate this framework via two canonical studies: (i) a thermodynamic continuous stirred-tank reactor (CSTR) model solving governing ODEs, where a Softplus constraint strictly enforces the Second Law of Thermodynamics; and (ii) an information-theoretic financial market model solving the inverse Fokker-Planck PDE to infer latent drift and diffusion","title":"Physics-Informed Deep Learning for Entropy Prediction in Heterogeneous Systems: Thermodynamic and Information-Theoretic Case Studies","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.01179"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:49957ff5ffb306a06f4325a22531f0b2e5a886e600336c72a3f981f0fe4a890ae6b8b7c770a0af9bfb6de408108c804b44357b66f1f5ccaadd4a36a6330b6c07","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.01179"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"a6556f1aa7a439ac929fd33e479579e11465280e6689440ffefc4d57bef29e6b","leaf_index":205569,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"fe9fd6c549fc18f127365a33c4e14c2b1e8f088b261797d2cbf6cfefad59b13d","side":"left"},{"sibling":"c982bc6737b11a59f588df4a35dfba7d7897de8d681fb6582c3a65847e901464","side":"right"},{"sibling":"e400fd841f70ba4e318e0d56adce0d5605f53d6dff3a89d652bf4303c08084a7","side":"right"},{"sibling":"2fda830467b1c9adf437eff69141b3fe24818e1645c79a6230ffb790bdacca56","side":"right"},{"sibling":"2582647bc6472cff5fc49ceeab52131dd52c2e5b5d94c55bada6884a141ef8a5","side":"right"},{"sibling":"bf8fe4fbdd715e3289029a0a2b189d8a48f5c617f2f67bb5d06b20d4944520a0","side":"right"},{"sibling":"1e82068bd784779754cf4c7ebad995756b8568c4c3050604d6f3f530fe4825b9","side":"right"},{"sibling":"41924649fb2045a8eb1c76bcccd1d2cd8c7e0ab0bba7b07a79bf25a0c1677263","side":"right"},{"sibling":"21332ee1c3955bf1803955bf945ab0966ce5e0aa48d8642320cdbc044a72b935","side":"left"},{"sibling":"6620a5008acf732cd3e57b0f2d1437293e88366c2e5b175ebeb7d796fc1e0c62","side":"left"},{"sibling":"a82575bfb494af7afcc13aaae718afa6f74030f09d71b02819ea25efd4186fc4","side":"right"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_1f38907786464675df29a35ee3d26692d6cffb29e2d85e00c1b7711775ab4968"}}