The Thermodynamic Cost of a Final Boundary Condition: A Resource Theory of Informational Pruning and a Rank-Indexed Contextuality Conjecture
Author
Ian Staley
Abstract
In prior work I modelled the macroscopic development of a closed quantum system as a directed graph of coarse-grained histories on which a final boundary condition induces an admissible subgraph. That programme never joined its pruning half to its contextuality half, nor assigned pruning a thermodynamic cost. This paper addresses both. I construct a resource theory whose objects are two-boundary-conditioned decoherent-history ensembles, whose free objects are those in which the terminal condition leaves the history distribution unchanged, and whose free operations are boundary-compatible coarse-grainings. Theorem 1 establishes that the relative entropy of the conditioned against the unconditioned history distribution is a faithful monotone under every such coarse-graining, jointly convex in the pair of distributions; a counterexample shows that the more obvious counting-based deficit is not. Theorem 2 establishes that a register satisfying the Reeb-Wolf hypotheses deposits heat at least kBT ln[n0 / (rαrω)] for equidistributed history weights, so lower terminal rank raises the derived cost floor. This is a floor and not a total ordering. I then advance, explicitly as a conjecture, a rank-indexed bridge to contextuality. I do not claim the universe erases histories; the more limited claim is that a register implementing admissibility filtering pays a rank-graded cost.
Keywords
decoherent histories; final boundary conditions; quantum resource theories; Landauer's principle; quantum contextuality; quantum foundations
Full Text:
References
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