Friction as the Cost of Probabilistic Computation: A Generalised Substrate Theory

Paper 1 in the Friction Theory paper-series. The foundational substrate theory: friction as the information-processing cost of probabilistic computation in any race architecture (parallel evaluation of competing candidate states under bounded resources with irreversible commitment). Behavioural Friction Theory (Paper 0) is recovered as the biological instantiation.

Abstract. Friction Theory (FT) treats friction as the information-processing cost of probabilistic computation in any race architecture. The substrate-universal claim — friction in any race substrate decomposes into magnitude, distribution, and rhythm — is tested on three large language model architectures (Cogito-671B, Qwen3-235B, Llama-3.3-70B) with a paired Qwen2.5-32B base-vs-instruct comparison. Seven empirical signatures replicate cross-architecture: iterative-pipeline dynamics matching the 1/e secretary-problem optimum; parse-vs-generate phase decomposition; constructive versus destructive friction types; friction profiles as cognitive fingerprints; mode-shift entry/exit costs; reactance as thermodynamic hysteresis that tracks RLHF intensity (with format-violation as the cleanest substrate-level demonstration); and trailing-task forgetting under high mid-task load (d = 1.2). Cross-substrate evidence from Saigusa et al. (2008) (Physarum) and Laibson (1997) places these findings within a six-substrate temporal-horizon gradient.

Version 2 (2026-05-20). Additions:

• §7b — Kubo (1966) fluctuation–dissipation anchor for the architectural-necessity argument: the rational agent ("Econ") is not merely empirically rare but thermodynamically forbidden as the limit of a sequence no finite-temperature substrate can complete (third law).
• §5.6.5 — empirical anchor from Paper 4B (Experiment 3) for commit-pressure as a substrate property: elaborated demonstrations both reduce per-token CR and improve accuracy in paired tests.
• §6.1b — empirical anchor from Paper 4B (Experiment 4) for reactance isolated from content effects via format mismatch (per-token CR signature + accuracy collapse).
• §9.5 — empirical anchor from Paper 4B (Experiment 5) for anticipatory friction in language-model substrates as a thin-window effect, consistent with the substrate-clock prediction.
• §9.5 — a new open question on the discounting measure dμ in the Net Friction Rule for memoryless substrates (single-event-bounded inference systems as the limiting case).
• Bibliography updated (Kubo 1966 added; cross-paper DOI currency).

Editorial revision throughout.

Companion papers in the Friction Theory series:

• Paper 0 (Behavioural Friction Theory master): 10.5281/zenodo.19462499
• Paper 2 (Capacity scaling): 10.5281/zenodo.20013491
• Paper 2B (In-context learning as working memory, fine-tuning as long-term memory): 10.5281/zenodo.20145218
• Paper 3 (Friction-guided inference): 10.5281/zenodo.20014121
• Paper 5 (Field-theoretic taxonomy of emotions): 10.5281/zenodo.20058825
• Paper 10 (Race architecture across substrates): 10.5281/zenodo.20014567
• Paper 13 (Operational Friction Theory): 10.5281/zenodo.20059876
• Paper 14 (Logic as Reactance): 10.5281/zenodo.20217712
• Paper 4 / 4B / 6 / 8 / 8b / 8c / 9 — in preparation