# Unifying Kibble–Zurek Mechanism in Weakly Driven Processes

## TL;DR

This paper introduces a new framework for the Kibble-Zurek mechanism that eliminates the need for ad hoc assumptions while preserving key characteristics.

## Contribution

A new framework is introduced that unifies the Kibble-Zurek mechanism without relying on ad hoc hypotheses.

## Key findings

- The Kibble-Zurek scaling for excess work is approximately 2/5.
- The result applies to both open and thermally isolated systems.
- The framework is demonstrated using four distinct scaling functions.

## Abstract

A description of the Kibble–Zurek mechanism with linear response theory has been done previously, but ad hoc hypotheses were used, such as the rate-dependent impulse window via the Zurek equation in the context of no driving in the relaxation time. In this work, I present a new framework where such hypotheses are unnecessary while preserving all the characteristics of the phenomenon. The Kibble-Zurek scaling obtained for the excess work is close to 2/5, a result that holds for open and thermally isolated systems with relaxation time that diverges at the critical point and the first zero of the relaxation function is finite. I exemplify the results using four different but significant types of scaling functions.