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Thermodynamic Computing and Substrate Independence

This project runs its architecture on GPUs. The question on this page is whether the result would change on other hardware. If the architecture’s measured properties survive a move to a different physical substrate, such as spiking neuromorphic chips or thermodynamic p-bit samplers, that is evidence for substrate independence. If they do not survive, that is evidence against it. Either result is worth having.

The success criterion is narrow on purpose. The test is whether the properties the project has already verified survive the change. Those properties are the vector representations that carry the stimulus, and the chain from the observation map to the tectum content. It is not a claim that a new substrate improves any emergence metric. None of the project’s 16 instruments is trusted yet, so no such claim could be checked.

The theory this architecture follows does not settle the question in advance. Todd Feinberg and Jon Mallatt, whose six neurobiological features shape the design, argue in a 2026 commentary in Behavioral and Brain Sciences that the physical substrate of a complex system is critical for sentience to emerge. On their view, a change of substrate can change more than speed and cost. The project uses their features as an architectural blueprint and does not claim their support for substrate independence. A positive result here would show that some measured properties survive the move. It would not show that the new substrate feels anything.

Thermodynamic Console Software emulation
0.000Energy / spin
0.000Magnetization

This visualization runs a software emulation in your browser. Physical thermodynamic hardware is not integrated. Full statement.

What the three views show

Ising lattice. Each square is a p-bit, a spin that is either up (orange) or down. A spin looks at its four neighbors and the field, then goes up with probability (1 + tanh(h / T)) / 2. That is the update rule for p-bits from Camsari and colleagues. Near the Onsager temperature, 2.269, the lattice forms domains at every scale. Below it, one direction wins. Neighboring spins never update at the same time. The lattice is split into a checkerboard, and the two colors take turns. Updating everything at once is faster to write and samples the wrong distribution.

Kuramoto ring and sphere. Each dot is an oscillator with its own natural frequency. Coupling pulls them together, and the length of the orange line is the order parameter r. On the circle (D = 2), the oscillators drift apart below a critical coupling of about 1.6 and lock above it. The project’s workspace binding runs exactly this case, with its oscillators on a circle, following the artificial Kuramoto oscillatory neurons of Miyato and colleagues.

The sphere view (D = 3) shows the same rule with each oscillator as a point on a sphere, turned by its own rotation. The binding code supports this, but the running architecture does not use it. The sphere behaves differently. It has no threshold, and order appears as soon as the coupling is switched on, as Chandra, Girvan and Ott showed for odd dimensions. Drag the sphere to turn it.

Sampling vs descent. Both lattices start from the same random state. Descent without noise freezes quickly with domain walls it cannot remove. Sampling with a slowly rising gain usually removes more of them and reaches a lower energy. Thermodynamic hardware is built around this property. Its noise lets a system leave a poor local minimum.

The cost of simulating continuous time on a clock

Biological neural dynamics are continuous, asynchronous and parallel. A GPU simulation cuts time into steps of fixed size, so the cost grows with the number of steps times the number of units. Each belief update in a trained model is a forward pass, a backward pass and a weight update. A data center GPU draws between 250 and 700 W. The human brain runs on about 20 W.

The brain is not free to run. It pays in metabolic energy for every spike. The difference is in the cost structure. In tissue the dynamics are the physics, and in a GPU the physics has to be computed.

Thermodynamics and the free energy principle

Karl Friston’s free energy principle describes living systems as minimizing variational free energy, a quantity that bounds surprise. It is tempting to say that thermodynamic hardware does this physically. That is not correct as stated, and the reason is below.

A p-bit chip samples from a Boltzmann distribution of whatever energy function is programmed into it. That is a fact about the hardware. It becomes inference only after an inference problem is compiled onto the chip’s couplings. Whether this project’s generative model can be compiled that way, and at what approximation cost, is an open question. It is a hypothesis this project can test. It is not a property the hardware already has.

Readiness levels

Level Status Technologies Evidence
1. Production Deployed and measured GPU tensor emulation, surrogate gradients, Brian2 comparison Behavioral task metrics and perception probes in the research repository; instrument statuses in the inventory (0 of 16 trusted)
2. Neuromorphic Research systems, no data from this project Intel Loihi 2, SpiNNaker 2, BrainScaleS-2, the NIR exchange format Published third-party benchmarks
3. Thermodynamic Early hardware for early partners, open-source simulators Extropic X0 and Z1 (Z1 early access planned for 2027), Normal Computing CN101 Vendor figures; open-source THRML, Torx and thermox simulators

Extropic states its Z1 chip carries 269,568 p-bits in eight cores, with 215,904 programmable couplings, a sparse graph of 16 neighbors per p-bit, sampling above 50 MHz, and under 1 W per die. Those are vendor figures. This project has not measured them.

What the project is building

The research code has an isolated package for this work, models/thermodynamic/. Phases 1 and 2 were merged on 2026-09-22. Phase 1 holds a p-bit emulator that updates one color class of the coupling graph at a time, tested against exact Boltzmann statistics, and a free energy relaxation solver tested against closed-form posteriors. Phase 2 adds a bridge between continuous values and spike trains, a stand-in driver for tests, export of spiking layers to the NIR exchange format, and an optional link to Extropic’s open-source THRML sampler, checked against the same exact statistics. A guard test keeps the package out of every production path, so nothing on this page can change a training run.

No result from the package is reported here yet. The next phase measures what the emulation costs and whether the verified properties survive it. Physical hardware is not part of the plan until it is available.

What this is and what it is not

The console is a software emulation that runs in your browser. It is not connected to any thermodynamic or neuromorphic chip, and it does not run the project’s architecture. The lattice is a textbook ferromagnet and the ring is the textbook Kuramoto model, chosen because their behavior is known exactly and you can check it by eye.

Nothing here is evidence that the architecture is substrate independent. That evidence can only come from running the verified parts of the architecture on another substrate and measuring them the same way. For the chip that has already flown, read about Intel’s Loihi in orbit. For the case for putting minds off planet, see Consciousness to Orbit. For a spiking network you can run now, open the Substrate Console.

Sources

  • Camsari, K. Y., Faria, R., Sutton, B. M., Datta, S. (2017). Stochastic p-bits for invertible logic. Physical Review X 7, 031014. arXiv:1610.00377
  • Onsager, L. (1944). Crystal statistics. I. A two-dimensional model with an order-disorder transition. Physical Review 65, 117.
  • Kuramoto, Y. (1984). Chemical Oscillations, Waves, and Turbulence. Springer.
  • Chandra, S., Girvan, M., Ott, E. (2019). Continuous versus discontinuous transitions in the D-dimensional generalized Kuramoto model. Odd D is different. Physical Review X 9, 011002. arXiv:1806.01314
  • Miyato, T., Löwe, S., Geiger, A., Welling, M. (2025). Artificial Kuramoto Oscillatory Neurons. ICLR 2025. arXiv:2410.13821
  • Feinberg, T. E., Mallatt, J. (2026). Sentience, emergence in neurobiological systems, and the prospects for artificial consciousness. Behavioral and Brain Sciences, commentary. Cambridge Core
  • Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews Neuroscience 11, 127-138.
  • Raichle, M. E., Gusnard, D. A. (2002). Appraising the brain’s energy budget. PNAS 99, 10237-10239.
  • Rouleau, N., Levin, M. (2026). Brains and where else? Mapping theories of consciousness to unconventional embodiments. Phil. Trans. R. Soc. A 384, 20250082.
  • Pober, J., Schwitzgebel, E. (2026). Substrate Flexibility and the Copernican Principle of Consciousness. Draft.
  • Extropic (2026). From One to One Billion: Torx, Thermalizers, and Z1.
  • Normal Computing (2025). Tape-out of the CN101 thermodynamic computing chip.
  • Pedersen, J. E. et al. (2024). Neuromorphic intermediate representation. Nature Communications 15, 8122.
  • NVIDIA. A100 and H100 data sheets (250 to 700 W by model and form factor).