Description

In 1867, James Clerk Maxwell imagined a tiny intelligent being that could sort fast and slow molecules — seemingly violating the second law of thermodynamics. This playful thought experiment launched a 158-year quest that would ultimately unite statistical mechanics, information theory, and computational complexity into a single rigorous framework.

This book traces that journey from Maxwell’s original letter through Szilárd’s engine, Shannon’s information theory, Landauer’s erasure principle, and Bennett’s reversible computing, to the modern fluctuation theorems of Sagawa and Ueda. It then develops the DEMON framework, introducing complexity classes DEMON(f,g) that classify Maxwell’s demon protocols by their information complexity f(n) (bits acquired) and erasure complexity g(n) (bits erased).

Six theorems form the backbone of the theory: a fundamental erasure bound, a feedback efficiency theorem, a strict complexity separation, a containment result linking demons to P, a provably optimal quantum advantage via Grover’s algorithm (tight by the BBBV bound), and a dense hierarchy of complexity classes arising from quantum walks on lattices. Category-theoretic unification ties the framework together. Computational validation confirms all predictions with less than 1% error across six orders of magnitude. Five falsifiable experimental predictions — spanning trapped ions, superconducting circuits, and photonic platforms — provide a concrete roadmap for testing the theory.