Energy-native compute · TR-2026-05
Energy-Native Computation and the Price of a Reproducible Bit
A survey and research position, rendered as a paper you can question and run.
David Jean Charlot, PhD · Michael Hiner
1. Can energy and computation share one coordinate?
An embodied machine spends its energy on three accounts: actuation, arithmetic, and the conversion infrastructure that feeds both, converting a source into a rail, storing charge, moving heat, conditioning a supply into the clean, constant form digital logic expects. For a legged or manipulating platform the actuation account usually dominates the total; this paper prices the third account, the conversion chain in front of the compute, whose share a reader can compute for their own platform by multiplying the per-stage efficiencies of §2 (assumption a reader can replace: the stage list, and each stage's efficiency). Each step is a domain crossing, and each is a loss. This paper follows that idea to its limit, where the distinction between the energy system and the computer disappears. It is not exotic: a diffractive optical network performs its matrix multiply on the energy of the light passing through it[1], and a neuron computes on the same ion gradient that powers it.
2. What does a crossing cost?
Order every energy-to-compute scheme by the number of domain crossings $K$ between the source and the computational state variable. Efficiency is multiplicative in the crossings and improves as they are deleted: from S0 separated, through storage- and conditioning-collapsed rungs, to S5 identity, where the source variable is the state variable and $K=0$. S5 is real for photonics and biology, and for the ionic and thermal carriers this review located both halves in the literature but did not locate a device joining them in one coordinate (the databases and search terms are named in the defensive publication)[6,7].
3. Can you buy invariance back?
The spectrum has a diagonal that is a design law: every crossing you delete for efficiency is a crossing at which you could have re-clocked or restored state to enforce reproducibility. So the identity substrate is maximally efficient and maximally noisy. The move is to stop demanding bit-identity of the noisy microstate and demand invariance only of the attractor basin a dissipative substrate settles into. The settling is the error correction; independent noise averages out, and only a common-mode supply excursion over the barrier can move the committed label. Read it by running it: raise the barrier until the ensemble holds one basin, and watch the committed label go bit-exact even as the bits-per-device fall.
4. What does a reproducible bit cost?
Escape from a basin under supply noise of intensity $D_\sigma$ follows Kramers' rate[4], $r \propto e^{-\Delta E_b/D_\sigma}$, so holding the label over a commit window with failure probability at most $\varepsilon$ demands a minimum barrier, and (since each rejected perturbation dissipates the barrier it climbs back down) a minimum energy per invariant commit:
This is a Landauer-analog for reproducibility, distinct from Landauer's $k_BT\ln 2$ per erased bit[1]: Landauer prices erasure, this prices reproducibility. Spend less and the basins are too shallow to reject the noise. Whether the bound is tight, or can be beaten by a cleverer coarse-graining, is stated as the open question: a conjecture with a scaling argument, not a proved theorem.
5. Why does reversibility invert here?
The bound inverts a premise the low-power field treats as settled: reversible computing minimizes energy by not dissipating[2], but a non-dissipative substrate has no attractor basins and so preserves supply noise. Dissipation builds the basins that reject it. The substrate that earns crossing-free invariance is therefore minimally dissipative but deliberately not reversible. And it is not free: deep, well-separated basins occupy the state range at a coarser spacing, so information capacity per device falls as the barrier rises. Free invariance is paid in bits per device, the true Pareto surface. Try it above: Barrier too cheap breaks the label; Reversible has no basins at all.
6. Conclusion
Collapsing the crossings between a machine's energy and its state is the efficiency win, and it is also the reproducibility problem. The way out is to let dissipation build the basins that reject supply noise for free and to commit the basin label rather than the microstate, at a price with a thermodynamic floor. For Physical AI, which must be frugal enough to run in a body and reproducible enough to be trusted with one, that floor is the quantity worth knowing. The map is offered as an open commons, and the bound as a question worth settling.
7. What would move this?
The binding constraint is a thermodynamic floor, and it is the one number worth knowing. Collapsing the crossings between a machine's energy and its state is the efficiency win and the reproducibility problem at once. The resolution here is to let dissipation build basins that reject supply noise for free, and to commit the basin label rather than the microstate, which is reproducible, and which costs something. That cost has a floor set by physics rather than by engineering, and it is the one term in this design that no better implementation removes.
What would move it. Not the floor. What moves is how far a real device sits above it, and that is the figure to report: measured joules per committed label against the bound, on named hardware. A design that closes on the floor has finished; one sitting orders of magnitude above it has an engineering problem with a known target, which is far more useful than an efficiency ratio against a competitor.