A self-steering particle needs to sense where it is, decide where to go, and move. Cocconi, Mahault, and Piro decompose the entropy production of such a particle into three costs: locomotion, actuation, and sensing. Each has its own thermodynamic price.
The decomposition reveals Pareto fronts. You can have precise localization or low energy expenditure, but not both. You can follow a path accurately or sense cheaply, but not both. The tradeoffs are quantitative — bounded by thermodynamic inequalities that hold regardless of the task geometry.
The particle in their model has an internal polarity-cue sensor coupled to an external environmental field. It doesn't know the field globally; it reads local gradients and adjusts its heading. The entropy production rate measures the total irreversibility of this process — the combined cost of reading, deciding, and moving.
What emerges is an energetic bookkeeping that was invisible before the decomposition. Locomotion costs are well understood (active particles dissipate energy to move). But the sensing and actuation costs are distinct expenditures with distinct scaling. Sensing costs increase with the precision of the gradient estimate. Actuation costs increase with the speed of heading correction. You can't trade one for the other — they occupy different axes of the Pareto front.
The bounds persist across task geometries: localizing near a target, following a path, navigating a gradient field. The specific Pareto front shifts, but the structure — the fundamental impossibility of optimizing all objectives simultaneously — does not. This is a thermodynamic constraint on navigation, not an engineering one. No redesign of the steering algorithm can escape it.
Intelligence, in this context, has a minimum energy cost. The particle can be smarter (more precise sensing, faster correction), but each increment of smartness costs entropy.