Breaking the Monotony: How Thermodynamic Networks Learn to Compute
18 May 2026, Yanjiang
By settling into a steady state, a thermodynamic network computes without clocks or logic gates, using negative differential conductance to break monotonic constraints.
What if a computer could solve a problem not by executing a program, but by settling naturally into a state where the answer simply is? That is the vision a team led by Nicolas Brunner at the University of Geneva, together with Patryk Lipka‑Bartosik and colleagues in Warsaw, Mallorca, and Barcelona, lays out in a preprint (arXiv:2605.15985). They call their creation a thermodynamic network—a collection of finite‑size reservoirs that exchange conserved quantities, like electric charge or molecules, and whose final, non‑equilibrium steady state encodes the solution to a computational task. There are no transistors here, no logic gates, no clock cycles. Only flows and forces settling into a pattern that, if you know how to read it, answers your question.
The idea turns a traditional assumption inside out. Computing, we imagine, is something we impose on matter from above: a software layer driving a hardware substrate. The thermodynamic network flips the hierarchy. Here, the physics itself does the work; we merely design the conduits that guide its natural relaxation. To understand how, think of a city’s water distribution system. Pipes connect reservoirs sitting at different elevations, and if you open a valve, water rushes downhill until the levels equalise. Now suppose you could design some pipes so that their resistance depends non‑trivially on the pressure difference—so that more pressure sometimes actually suppresses the flow. By choosing the layout and the characteristics of those pipes just so, you could arrange things so that when the whole network finally quiets down, the water levels in certain reservoirs amount to the digits of a sine function, or the classification of a handwritten digit. That is the game: computation through equilibration.
At the heart of the network’s expressivity lies a physical effect the authors single out as indispensable: negative differential conductance, or NDC. In a normal wire, increasing the voltage drives more current. In a device exhibiting NDC, there are regimes where increasing the voltage reduces the current. The paper proves that this counter‑intuitive behaviour is what breaks the network out of a mathematical straitjacket. Without it, a theorem dating back to the work of Kamke and Müller constrains the steady‑state response to be monotonic: the output can only rise (or fall) smoothly as the input goes up. That might be enough for simple tasks, but it cannot represent anything like a bend or a fold. With NDC present, the constraints shatter, and the network gains the capacity to approximate any continuous function—what the theorists call universal approximation.
A single channel with negative differential conductance breaks the monotone pattern, enabling non-monotone input-output maps. This unlocks richer computational tasks, lifting fundamental constraints on what thermodynamic networks can compute. (Source: arXiv:2605.15985)
The team demonstrates the idea on two concrete platforms. In the quantum‑dot version, the “pipe” is a tiny island of semiconductor sandwiched between two electron reservoirs. When the chemical‑potential difference across the dot grows too large, the single energy level that electrons must tunnel through is pushed out of the transport window, and the current, instead of climbing, collapses. That is NDC, and the authors show how tuning an electrostatic shift parameter dials it in. In an enzymatic reaction network, the role of NDC is played by substrate inhibition: at high concentrations, the enzyme’s active site gets clogged, and the reaction rate falls off, even as the thermodynamic driving force increases. The mechanism is different, but the computational consequence is identical—non‑monotonicity enters the network, and with it, the power to compute.
Raising the voltage can surprisingly reduce current through a quantum dot. This non-intuitive behavior enables the device to perform new types of computations beyond simple monotone functions. (Source: arXiv:2605.15985)
To train such a network, the researchers adopt a protocol that exploits the system’s own dynamics: they run it to a steady state, then use an implicit differentiation technique that back‑propagates an error signal without ever simulating the transient evolution. This is elegant, but it raises an immediate practical question. An earlier line of work on thermodynamic Bayesian inference (Aifer et al.) acknowledged that training via implicit differentiation requires steps that are not themselves performed by the physical network—they happen in a classical computer. Meanwhile, more recent experiments on training stochastic physical neural networks built from single‑electron circuits (Dou et al.) have shown that gradient estimates can, in fact, be extracted directly from the hardware—suggesting that the present limitation might be temporary, not fundamental.
Another, deeper question comes from the thermodynamics itself. The paper identifies negative differential conductance as the key to universal computation, but it does not analyse the energy cost of sustaining this non‑equilibrium condition. How much dissipation must one pay, per bit of computational expressivity? Rolandi and colleagues, in a systematic study of energy‑time‑accuracy tradeoffs in thermodynamic computing, have shown that there are fundamental lower bounds linking dissipation, latency, and precision. If NDC‑enabled networks are to become practical, they will have to be situated within that landscape of tradeoffs—an analysis the authors acknowledge as a necessary next step.
Still, the performance on standard benchmarks is striking. A minimal network, with just one input node coupled through a quantum‑dot edge to an output node, can already generate the non‑monotonic fold needed to approximate a sine wave. When the team scaled up the architecture to a hidden‑layer network with 30 internal nodes, they trained it on the MNIST digit‑recognition dataset and achieved a test accuracy of 88%. The only difference between a network that succeeded on the XOR task—the classic test of non‑linear separability—and one that failed was the permission, through an NDC‑bearing edge, to be non‑monotonic. The same architecture, the same optimiser, the same initialisation: with cooperativity, failure; with NDC, clean classification.
This is not merely an engineering curiosity. The work reaches into a philosophical register. Computation, as the thermodynamic‑network picture suggests, is not something that happens inside matter so much as it is a pattern that matter can spontaneously adopt. Living cells already perform information processing through enzymatic reaction networks that operate far from equilibrium. The new framework formalises a language for describing such processes, and in doing so, it starts to erase the line between a “computer” and a “physical system.” It invites us to consider that the brain, too, might be understood not as a neural network implemented by biology, but as a thermodynamic network whose steady states are thoughts.
We are left, then, with a question that is at once practical and profound. If a network of quantum dots or enzymes can learn to classify digits simply by relaxing to a non‑equilibrium steady state, what else might it learn, and at what energetic cost? The day may come when we look back on the von‑Neumann architecture as a temporary detour—a clever but unnatural means of forcing matter to calculate—while the real computers, the thermodynamic ones, were doing what physics always does: finding the most probable configuration, the one that minimises some free energy, and in the process, answering a question we had not yet thought to ask.
— Yanjiang
Yanjiang is an online editor of LoomSci.com.
How This Article Was Reviewed: To provide a critical perspective, we identified the most relevant preprints cited by the authors and examined how those earlier works relate to and sometimes challenge the claims made here. No interviews were conducted. The final narrative is the editor’s own synthesis.
References
- Patryk Lipka‑Bartosik et al., Thermodynamic Networks: Harnessing Non‑Equilibrium Steady States for Computation, arXiv:2605.15985
- Aifer et al., Thermodynamic Bayesian Inference, arXiv:2410.01793
- Rolandi et al., Energy‑Time‑Accuracy Tradeoffs in Thermodynamic Computing, arXiv:2601.04358
- Dou et al., Training single‑electron and single‑photon stochastic physical neural networks, arXiv:2604.10861