Limits of Computing with Matter: From thermodynamic bounds to a candidate cubic computer design

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. A mole of active matter, organized as a compact irreversible machine, cannot compute like a mole. The ceiling is geometric: power, control, and corrected results all cross the body's surface, so throughput scales with the two-thirds power of its matter while memory scales with its volume. At 100 MHz, a mole of silicon-equivalent sites offers 6.4×10³¹ candidate site-cycles per second; a thermal-noise reliability floor on switching energy and a 1.4 kW power budget support 7.6×10²⁰ raw transitions, eleven orders of magnitude fewer. And the binding scarcity turns out to be neither sites nor energy. It is moving corrected results across the surface. The paper makes this concrete with a reference object: a 27.5 mm laminated cube of 170 double-sided silicon leaves, just over one mole of matter, holding about 0.8 petabytes of resident state at a published 3D-NAND density. Under one effective-work accounting, the energy ceiling at 1.4 kW admits 3.5×10¹³ structured-layer evaluations per second, while the corrected-output ceiling admits about 1.2×10⁸ per TB/s of bandwidth. Output binds. The feasible role of most of the mole is memory. The cube is unbuilt and no performance is claimed. Instead, the study reduces feasibility to pass/fail gates at a tenfold performance-per-watt stress target over NVIDIA's B300: at least 32.5 TB/s of corrected output bandwidth, at most 56 fJ per multiply-accumulate, at least 3125 operations per resident byte, and at least 3.9×10⁹ independently scheduled evaluations per second. A standard-library Python script recomputes every number printed in the paper. The mole is the container. Its surface, its channels, and its stored configuration are the processor.