Symmetry vs Symmetry

TL;DR

This paper explores how different types of symmetry in parametrized systems evolve as parameters change, highlighting their contrasting behaviors and connections to entropy and symmetry breaking.

Contribution

It introduces a distinction between generic and specific symmetry, analyzing their opposite behaviors during parameter variation and their implications in physical systems.

Findings

Generic symmetry relates to entropy changes.

Specific symmetry involves symmetry breaking.

Contrasts between symmetry types are characterized.

Abstract

This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as the parameter changes: generic symmetry has links with entropy while specific symmetry has to do with symmetry breaking as it is usually understood in physics.