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We express the relativistic equation of state(EOS), $\\rho-\\rho_0=(\\gamma-1)^{-1}p$,\\ in the two equations: $\\rho=\\rho_0 f(\\lambda)$,\\ and $p=\\rho_0 g(\\lambda)$, where $\\lambda$\\ is a parameter related to the kinetic energy, hence the temperature, of the gas. In the both extreme limits, they give correct EOS:\\ $\\rho=3p$\\ in the ultra-relativistic, and\\ $\\rho-\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.3330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2011-03-17T03:36:45Z","cross_cats_sorted":[],"title_canon_sha256":"62e9bb351c6c09373a1388815934c7035858479540d05dc67b127e260c1d7a11","abstract_canon_sha256":"a8f8c5904c0a86f814990a0533e82aa0367e02153247eca944bdf1a2f421c809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:18.627432Z","signature_b64":"3DQmkBUQGC3CA+RjEImEANKUFLNnDjXK4iCn3F2B1cyh8hUM27Syl6OqScshGvsJbSnE7Qjdt+BPcKK3N867Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"478f8715aa68a1364beecd22373a1d509e92319aaeb2d1acc374a263c1539f6b","last_reissued_at":"2026-05-18T02:22:18.626743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:18.626743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"4-Velocity distribution function using Maxwell-Boltzmann's original approach and a new form of the relativistic equation of state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.SR","authors_text":"Prasad Basu, Soumen Mondal","submitted_at":"2011-03-17T03:36:45Z","abstract_excerpt":"Following the original approach of Maxwell-Boltzmann(MB), we derive a 4-velocity distribution function for the relativistic ideal gas. 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