Remarks on the structure of states of composite quantum systems and envariance

Yu Jing Guo, Jinchuan Hou

G. Scolarici

V. M. Akulin

Ph. Blanchard, Erwin Brüning

Sebastian Deffner, Wojciech H Zurek

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  with Hamiltonian  H 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.

Sebastian Deffner, Wojciech Hubert Zurek

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 S with Hamiltonian HS 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.