Informational Resolution Invariance and Projection-Induced Irreversibility in Thermodynamics

This paper reframes the Second Law of Thermodynamics as an algebraic consequence of informational invariance under scales of resolution. To ensure structural objectivity across varying observer resolutions, macroscopic evolution must remain invariant under arbitrary refinements of the coarse-graining scale. Microscopic dynamics are taken to be reversible and information-preserving (Liouville[1] or unitary evolution), while macroscopic behavior emerges by interleaving this trajectory with a non-injective projection. This resolution symmetry forces the macroscopic equations into an autonomous, closed structure. Thermodynamic irreversibility and entropy generation are thus derived as the mandatory geometric cost of maintaining scale-invariant stability, with the Third Law extending naturally from this framework.