Foundations of statistical mechanics from symmetries of entanglement

TL;DR

This paper introduces envariance, a symmetry of entangled quantum systems, to characterize thermodynamic equilibrium states without relying on traditional probabilistic concepts, providing a new foundational perspective.

Contribution

It demonstrates that thermodynamic equilibrium states can be fully characterized by envariance, offering a novel, probability-free approach to quantum statistical mechanics.

Findings

Microcanonical states are fully envariant under all unitaries

Canonical states derived from counting degenerate energy levels

Approach avoids ambiguous notions like ensemble and randomness

Abstract

Envariance -- entanglement assisted invariance -- is a recently discovered symmetry of composite quantum systems. We show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical equilibrium of a system $\mathcal{S} $ with Hamiltonian $H_\mathcal{S}$ is a fully energetically degenerate quantum state envariant under every unitary transformation. The representation of the canonical equilibrium then follows from simply counting degenerate energy states. Our conceptually novel approach is free of mathematically ambiguous notions such as ensemble, randomness, etc., and, while it does not even rely on probability, it helps to understand its role in the quantum world.