The Preservation Tradeoff: A Thermodynamic Bound in the Diminishing-Returns Regime

TL;DR

This paper introduces a thermodynamic bound on information preservation, formalizes a response function called preservation stiffness, and demonstrates its applicability across various physical and computational systems.

Contribution

It defines the preservation stiffness and derives the Stiffness-Odds Identity, providing a universal, substrate-agnostic diagnostic for thermodynamic efficiency in information preservation.

Findings

Unconditional bound on preservation efficiency: κ* < 0.50.

Optimal preservation constrained to a 30-50% efficiency band for certain regimes.

Framework consistent with biological and network systems like E. coli and TCP/IP.

Abstract

Thermodynamic systems that preserve information against thermal fluctuations face a tradeoff distinct from transmission (Shannon) or erasure (Landauer). We formalize the preservation problem by defining the preservation stiffness $S_\kappa$, a response function analogous to magnetic susceptibility, and derive the Stiffness-Odds Identity: at optimal allocation, the stiffness equals the ratio of payload to maintenance capacity. This identity is the paper's central contribution. It reduces optimal preservation to a single measurable response variable and provides a substrate-agnostic diagnostic for thermodynamic efficiency -- applicable wherever maintenance competes with payload, regardless of whether the underlying substrate is biochemical, electronic, or algorithmic. For all systems in the diminishing-returns regime, we prove the unconditional bound $\kappa^* < 0.50$. For the subclass exhibiting smooth saturation with rate parameter $a \in [2,3]$ -- an empirically characterized efficiency frontier, not a universal constant -- the optimum is further constrained to the 30-50% band. We motivate this functional form from two independent physical principles: Shannon error exponents and thermodynamic dissipation bounds. We then illustrate consistency with representative operating points from kinetic proofreading in E. coli and protocol overhead in TCP/IP networks, and specify conditions under which the framework is falsifiable.