V01.09 — Mirror Physics III: Thermodynamic Observerhood

This paper is the third paper in the Physics Support Arc of the Mirror Programme, Volume I: Observerhood. It follows V01.07 — Mirror Physics I: Constraint Propagation and the Physical Conditions for Observerhood and V01.08 — Mirror Physics II: Constraint Salience and Physical Coupling. Mirror Physics I identified causal order, local substrate persistence, metastable memory, thermodynamic throughput and error-corrective repair as support conditions for observer-continuity. Mirror Physics II introduced constraint salience as a scale- and horizon-relative organisational quantity, while refusing to treat it as a new field or force. The present paper develops the thermodynamic side of that sequence. The paper argues that an observer is not merely an information-processing structure, but a thermodynamically maintained constraint structure. A physically realised observer must spend resources to preserve memory, correct error, maintain boundaries, regulate update and sustain identity across time. The paper introduces a persistence-cost functional decomposed into memory, correction, boundary, update and audit costs, and states a thermodynamic observerhood condition: reliability tracking and self-model governance become observer-relevant only when their expected viability contribution exceeds their physical and computational maintenance cost. The analysis is deliberately conservative. It does not modify thermodynamics, relativity or quantum theory. It identifies the cost structure that any physically realised observer must satisfy.