Einstein's Field Equations From the Entropy Framework

This document demonstrates that the entropy density field framework satisfies all three conditions of Jacobson's (1995) thermodynamic derivation of the Einstein field equations: (1) entropy proportional to horizon area, (2) the Clausius relation δQ=TdSδQ=TdS, and (3) the equivalence principle. The framework provides physical grounding for each condition—deriving area-proportional entropy from entropy criticality at the horizon, grounding the Clausius relation in Landauer's principle, and explaining the equivalence principle via the universality of structural information cost. Through Birkhoff's theorem and the Newtonian limit supplied by the entropy field, the Schwarzschild metric and Bekenstein–Hawking entropy follow without presupposing the Einstein equations. Jacobson's derivation then yields the complete Einstein field equations, including an identification of the cosmological constant with the entropy decay rate: Λ=3λ/DΛ=3λ/D. This closes the largest theoretical gap in the entropy framework, establishing it as a thermodynamically complete alternative foundation for general relativistic phenomenology at the classical level. DISCLAIMER Generative AI was used to assist with literature screening / coding support / draft language revision. All AI-assisted outputs were independently checked by the author, and the author takes full responsibility for the final analysis and text. This is encompassing all the work that has been done and will be done. All code is under MIT licensing. All research papers are under Creative Commons License. All code, outputs and notes are included in the reproducibility bundle zip file.