Ten reasons why a thermalized system cannot be described by a many-particle wave function

TL;DR

The paper argues that thermalized systems cannot be fully described by many-particle wave functions, emphasizing the fundamental stochasticity and irreversibility in statistical mechanics, and proposes wave packets as a more appropriate representation.

Contribution

It challenges the common assumption of deterministic wave function evolution in thermalized systems, highlighting the necessity of stochasticity and proposing wave packets as a better model.

Findings

Thermalized systems are better represented by localized wave packets.

Wave packets must re-localize after scattering, implying inherent stochasticity.

Irreversibility in statistical mechanics is a fundamental property of nature.

Abstract

It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of statistical mechanics. The usual attempts to resolve this conflict for instance by appealing to decoherence or eigenstate thermalization are riddled with problems. This paper considers theoretical physics of thermalized systems as it is done in practise and shows that all approaches to thermalized systems presuppose in some form limits to linear superposition and deterministic time evolution. These considerations include, among others, the classical limit, extensivity, the concepts of entropy and equilibrium, and symmetry breaking in phase transitions and quantum measurement. As a conclusion, the paper argues that the irreversibility and stochasticity of statistical mechanics should be taken as a true property of nature. It follows that a gas of a macroscopic number $N$ of atoms in thermal equilibrium is best represented by a collection of $N$ wave packets of a size of the order of the thermal de Broglie wave length, which behave quantum mechanically below this scale but classically sufficiently far beyond this scale. In particular, these wave packets must localize again after scattering events, which requires stochasticity and indicates a connection to the measurement process.