Limits of Computing with Matter: From thermodynamic bounds to a candidate cubic computer design
Year: 2026
Type: article
Abstract: If every atom in a mole became a switch, would you get a computer with 6·10²³ switches' worth of power? This paper argues no. The ceiling is physical: nine stated postulates cap a compact body's compute throughput through the heat it can remove and a floor on switching energy, so throughput scales with the two-thirds power of its matter (its surface) while memory scales with its volume. A third bound identifies the scarce resource as independently controllable channels: a tabletop body has about 10¹⁶ of them, seven orders of magnitude fewer than its atoms. Assembled, these laws cut the naive mole expectation by twelve orders of magnitude, to 10²⁴–10²⁵ switching events per second. As a corollary, the same bounds admit a 2.75 cm laminated cube of 3D-NAND-style cells, each one a weight bit and a switch at once. On the paper's cell-level accounting the cube projects to roughly 2,400× the throughput of a 2025-flagship GPU at 85 kW, with 39× less energy per switching event; de-rated to demonstrated practice in every projected step simultaneously, it still delivers 110–220×. The mole is the container. Its surface, its channels, and its stored configuration are the processor.
Author: Amberg, Max-Josef
Institution: University of Bern
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169666724
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