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

We introduce Friction Theory (FT), a substrate-universal account of friction as the thermodynamic cost of probabilistic computation in any system that performs parallel evaluation of competing candidate states under bounded resources with irreversible commitment. Behavioural Friction Theory (BFT; Pødenphant Lund 2026a) is recovered as the biological instantiation of FT for mobile, mortal, metabolically-constrained organisms. The formal relation is BFT ⊂ FT. Friction in any race architecture decomposes into exactly three dimensions: magnitude, distribution, and rhythm. The framework 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 signatures of in-session budget allocation are recovered: iterative-pipeline dynamics matching the secretary problem's 1/e ≈ 36.8% optimum; parse-vs-generate phase decomposition; constructive vs destructive friction types; friction profiles as cognitive fingerprints; mode-shift entry and exit costs; reactance as thermodynamic hysteresis tracking RLHF intensity (with format-violation as the cleanest substrate-level demonstration); and trailing-task forgetting under high mid-task load (d = 1.2, the strongest cross-model effect). Cross-substrate data from Saigusa et al. (2008) and Laibson (1997) position these findings within a six-substrate temporal-horizon gradient (LLMs, Physarum, C. elegans, Drosophila, cephalopods, mammalian brains). Classical cognitive biases — anchoring, confirmation, sunk cost, loss aversion — are reinterpreted as thermodynamic necessities in any race architecture, extending the resource-rationality tradition. A deeper unification (§5.8) connects Kahneman's peak-end bias, dopaminergic reward-prediction error, Friston's free energy minimisation, and attention-weighted saliency in transformer LLMs (ρ = +0.17 between token surprise and downstream attention, empirically confirmed on Qwen2.5-0.5B) as substrate-specific signatures of one mechanism: surprise-weighted state retention. Hysteresis is reframed as the structural precondition for learning in any bounded probabilistic system.