New physics research reveals a surprising asymmetry: running a neural network – the 'thinking' part – could theoretically cost zero energy, but teaching it – the 'learning' part – always burns a few quanta of energy per fact. The finding challenges our assumptions about the energy efficiency of both artificial and biological brains.
The research
Physicist Alexei V. Tkachenko (affiliated with Brookhaven National Laboratory and the Initiative for the Theoretical Sciences, as per the preprint's metadata) published a paper in March 2025 on arXiv, with the latest revision in August 2026. He constructed a mathematical model of a feedforward neural network, the most common type used in AI, and treated it as a physical system subject to the laws of thermodynamics.
Tkachenko found two exact bounds. First, if the network processes information infinitely slowly (quasi-statically), the work required for inference is exactly zero – regardless of input, weights, or bias. Second, at any finite speed, the energy cost is at least the squared Wasserstein-2 distance between the initial and final states divided by the duration. In practical terms, this means the energy cost of inference is set by how fast you change the state, and at the fastest usable speed, it's about k_B T per dimension of the widest layer – that's one unit of thermal energy per neuron.
Strikingly, learning is different. Writing parameters into the network incurs an irreducible cost of a few k_B T per weight and bias, and this cost survives even in the quasi-static limit. In simulations, the inference work saturated the transport bound within 4%, and accuracy collapsed once dissipated work fell below thermal scale.
Why it matters
This research provides a fundamental limit on the energy efficiency of any physical network, including biological brains. Your brain consumes about 20 watts, and this study suggests that the bulk of that energy isn't used for the act of thinking itself, but rather for learning and for maintaining the network (though this paper focuses on learning). For AI, it implies that the energy cost of running a trained network (inference) can be made arbitrarily small with clever engineering, but training new models will always cost a certain amount per parameter. This could guide hardware design: instead of optimizing arithmetic, focus on minimizing the energy of memory writes.
What you can do
For your own brain, this research highlights that learning new things is fundamentally more energy-intensive than recalling or using what you know. So when you're studying, don't be surprised if you feel mentally tired – that's the thermodynamic cost of learning. To maximize efficiency, space out your learning sessions to give your brain time to consolidate, and focus on understanding rather than rote memorization, which might reduce redundant parameter updates.
Source: arXiv q-bio.NC
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