Groupoid Semantics for Thermal Computing

TL;DR

This paper introduces a groupoid-based semantic framework for thermal computing systems, linking logical and thermal aspects, and reveals quantum semantics underlying classical models, with applications to encryption and quantum phenomena.

Contribution

It develops a novel groupoid semantics for thermal computing, providing an algebraic characterization of heat in encryption and a functorial classical model for quantum teleportation.

Findings

Algebraic characterization of heat in encryption functions

Reveals quantum semantics in classical models

Provides a functorial classical model for quantum phenomena

Abstract

A groupoid semantics is presented for systems with both logical and thermal degrees of freedom. We apply this to a syntactic model for encryption, and obtain an algebraic characterization of the heat produced by the encryption function, as predicted by Landauer's principle. Our model has a linear representation theory that reveals an underlying quantum semantics, giving for the first time a functorial classical model for quantum teleportation and other quantum phenomena.