Thermal equilibrium of a macroscopic quantum system in a pure state

Understand

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function.

• The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential.
• When this is true we say that the system is in macroscopic thermal equilibrium (MATE).
• Such a system may however not be in microscopic thermal equilibrium (MITE).