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

The Charlot Lab & The Hiner Lab · interactive companion · defensive publication DP-2026-02

explorable — the model is inline ask — grounded in this paper run — drive the method as you read on-device where available

In a low-power substrate, energy conversion and computation are frequently the same physical mechanism, described by two communities that do not cite each other. Order every scheme by the number of domain crossings that survive between the energy source and the computational state variable; collapsing them raises efficiency and, along the same diagonal, forfeits the interfaces at which reproducibility could have been enforced — so the most efficient substrate inherits the raw noise of its carrier. The position: buy reproducibility back without a crossing by committing the basin label a dissipative substrate settles into, not the microstate. Its price is a thermodynamic lower bound — a Landauer-analog for a reproducible bit.

1. One coordinate for energy and computation

An embodied machine spends most of its energy not on arithmetic but on the infrastructure around it: converting a source into a rail, storing charge, moving heat, conditioning a supply into the clean, constant form digital logic expects. 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 — and 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. The crossings-tax spectrum

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 empty-but-implementable for the ionic and thermal carriers, where both halves are already published[6,7].

3. The diagonal, and buying 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.

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Figure 1. The interactive companion, embedded in the argument. Independent per-element noise averages out; the barrier ΔE, priced against supply noise σ, sets whether the basin label is replay-identical.

4. The price of a reproducible bit

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:

$$ E_{\text{inv}} \;\ge\; \Delta E_b^{\min} \;=\; D_\sigma\,\ln(1/\varepsilon) + \text{const} \;\xrightarrow[\;D_\sigma\to k_BT\;]{}\; \Theta\!\big(k_BT\ln(1/\varepsilon)\big). $$

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. The reversibility inversion, and its cost

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.

This is a living paper — a pilot. The full report with figures and references is the Technical Report (PDF); the formal program is the CC0 defensive publication. References [1]–[9] resolve there. Ask the paper anything using the console →