Foundations of statistical mechanics from symmetries of entanglement

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.

12 pages; published version

References in corpus (3)

• Quantum Darwinism
• Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule
• Quantum probabilities from quantum entanglement: Experimentally unpacking the Born rule

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• Quantum Otto engines at relativistic energies
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• A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach