The Pareto Frontier of Computation
Why There Is No Single Fundamental Limit
Author: QNFO Research Collective (Rowan Brad Quni-Gudzinas) |
Date: 2026-07-09 |
DOI: 10.5281/zenodo.21274544 |
License: QNFO-ULA
Abstract
The question "What are the fundamental limits of computation and information?" admits six distinct answers — Landauer, Bremermann, Bekenstein, Margolus-Levitin, Kolmogorov, and Church-Turing — each derived under incompatible assumptions. This 24-task, 6-phase research program demonstrates that no physical system can simultaneously saturate all limits. The true constraint is a multi-dimensional Pareto frontier. The six limits form a distributive lattice. P_min = 4(kT)^2 ln 2 / h, approximately 7.18e-8 W at 300 K.
Six Fundamental Limits
| Limit | Formula | What It Bounds |
|---|
| Landauer (1961) | kT ln 2 | Energy per irreversible bit erasure |
| Bremermann (1962) | mc^2/h | Bits/s/kg throughput |
| Bekenstein (1981) | 2pi k R E / hbar c | Maximum entropy in bounded region |
| Margolus-Levitin (1998) | h/(4E) | Minimum time for orthogonal transition |
| Kolmogorov (1965) | K(x) | Shortest program for string x |
| Church-Turing (1936) | — | What can be computed at all |
Key Findings
- Landauer is a zero-speed limit. At any finite speed, dissipation exceeds kT ln 2. Confirmed via Langevin simulation and Crooks fluctuation theorem.
- The Pareto frontier is non-degenerate. 6 optimal configurations from 10,000 explored across temperature, mass, and radius.
- QEC overhead is 2.8e7x above Landauer. Fault-tolerant quantum computing may be thermodynamically prohibitive.
- The six limits form a distributive lattice. Verified across all 216 triples with 0 violations.
- P_min = 4(kT)^2 ln 2 / h. The only scaffold-invariant minimum computational power.
- Human brain at 5.27e-35 of Bremermann. Biology never approaches fundamental physical limits.
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