Typicality in the foundations of statistical physics and Born's rule

TL;DR

This paper clarifies the role of typicality in statistical physics and quantum mechanics, arguing that typicality is essential for deriving Born's rule and addressing misconceptions about its necessity and circularity.

Contribution

It provides a clear explanation of typicality's importance in justifying Born's rule, countering claims of circular reasoning and distinguishing it from relaxation to equilibrium.

Findings

Typicality is crucial for deriving Born's rule.

Relaxation to equilibrium is neither necessary nor sufficient for Born's rule.

The circularity claim against the typicality approach is unfounded.

Abstract

Typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. However, the role of typicality is not always appreciated. An example is the paper "Foundations of statistical mechanics and the status of Born's rule in de Broglie-Bohm pilot-wave theory" by Antony Valentini, where he presents typicality and relaxation to equilibrium as distinct approaches to the proof of Born's rule, while typicality is in fact an overriding necessity. Moreover the "typicality approach" to Born's rule of "the Bohmian mechanics school" is claimed to be inherently circular. We wish to explain once more in very simple terms why the accusation is off target and why "relaxation to equilibrium" is neither necessary nor sufficient to justify Born's rule.