A Kinetic Theory of the Gated Self-Evolving LLM Agent

We find traces of fluid dynamics in the self-evolution of an LLM agent, and give the kinetic theory that predicts them. Gated self-evolution is the loop in which an agent rewrites its own skills under a validation gate. Self-evolution research has treated the agent as the unit; we study instead the individual instances inside it. Here the agent is DSH-plugin-based: it runs in production on DeepSeek Harness (DSH), and its plugins satisfy four architectural properties (permutation symmetry, reversibility, acyclicity, typed contracts), which license treating these instances as identical hard spheres; the theory is accordingly scoped to DSH-class plugin populations. On this scope the paper builds three theory layers. The rigorous layer, independent of any analogy, comprises an any-time hitting-time certificate bounding the expected rounds to any prescribed improvement, a resolution law that prices held-out validation budgets, and a separation theorem: the daemon must stay outside the population, because merging evaluator with evaluated voids the certificate. The kinetic layer is a master equation over the plugin × version × task grid with four operators (collision, reaction, external field, gate), where collision is co-activation. Its moment hierarchy, the step that turns a gas into fluid equations, generates the falsifiable statistical signatures. Throughout, the fluid reading is a bounded analogy: momentum is not conserved, so no Navier–Stokes limit exists. The measured layer runs on a faithful minimal instance, a large library of four-parameter skill plugins retrieved one per episode with a co-activation probe, in a one-model, one-task-family WebShop environment; every element maps to the DSH loop by architectural role. Population fluctuation scaling is density-gated: invisible at sparse edit density, it emerges at the predicted rate under tripled density, as directional evidence.