Amadeus Brandes

1paper

1 Paper

STAT-MECHDec 29, 2025
The Preservation Tradeoff: A Thermodynamic Bound in the Diminishing-Returns Regime

Amadeus Brandes

Thermodynamic systems that preserve information against thermal fluctuations face a tradeoff distinct from transmission (Shannon) or erasure (Landauer). We establish a feasibility condition for this preservation problem within a broad class of systems exhibiting diminishing returns in error suppression. By defining the preservation stiffness S_kappa, a response function analogous to magnetic susceptibility, we derive an optimality condition linking S_kappa to the resource odds. This identity provides a substrate-agnostic diagnostic: deviations reveal thermodynamic inefficiency or operation outside the smooth reliability regime. For systems in the diminishing-returns regime -- a class we argue is typical of physically realistic error-correction -- the optimal maintenance allocation is bounded above by 50%; for the physically significant subclass exhibiting smooth saturation, it is further constrained to a 30-50% band. We derive this regime from two independent physical principles -- Shannon's channel capacity and Landauer's erasure bound -- whose convergence on the same functional form constitutes our central theoretical contribution. We validate this framework against kinetic proofreading data in E. coli and protocol overhead in TCP/IP networks, and specify conditions under which the prediction is falsifiable.