The Maximal Entanglement Limit in Statistical and High Energy Physics

Abstract

These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a Maximal Entanglement Limit (MEL) in which phases of quantum states become unobservable, reduced density matrices acquire a thermal form, and probabilistic descriptions emerge without invoking ergodicity or classical randomness. Within this framework, the emergence of probabilistic parton model, thermalization in the break-up of confining strings and in high-energy collisions, and the universal small $x$ behavior of structure functions arise as direct consequences of entanglement and geometry of high-dimensional Hilbert space.

final published version; 70 pages, 11 figures; Lectures at the 65th Jubilee Cracow School of Theoretical Physics, Zakopane, Tatra mountains, Poland, June 14-21, 2025