Foundations of Temperature Theory

TL;DR

This paper rigorously analyzes the classical concept of temperature in combinatorial game theory, providing proofs of fundamental properties and exploring the relationship between game value and thermograph.

Contribution

It offers precise proofs of core temperature properties and investigates the link between game value and thermograph in classical combinatorial temperature theory.

Findings

Proves existence of temperature in combinatorial games

Establishes order-preservation of temperature

Explores the relationship between game value and thermograph

Abstract

Temperature of combinatorial games have been long studied since when Conway established the modern combinatorial game theory, and there are several variations of the concepts. In this article, we focus on one of the classical versions of temperature, and give precise proofs to the fundamental claims on temperature, namely, the existence, order-preservation, and homomorphism. Besides, a general relationship between the value and the thermograph of a game is investigated.