This question can be formalized by considering the quantum mechanical density matrix ρ of the system. If the system is divided into a subregion A (the region being probed) and its complement B (everything else), then all information that can be extracted by measurements made on A alone is encoded in the reduced density matrix ρ ρ A = Tr B ⁡ ⁡ ρ ρ ( t ) . If, in the long time limit, ρ ρ A ( t ) approaches a thermal density matrix at a temperature set by the energy density in the state, then the system has "thermalized," and no local information about the initial condition can be extracted from local measurements. This process of "quantum thermalization" may be understood in terms of B acting as a reservoir for A. In this perspective, the entanglement entropy S = − − Tr ⁡ ⁡ ( ρ ρ A log ⁡ ⁡ ρ ρ A ) of a thermalizing system in a pure state plays the role of thermal entropy. Thermalizing systems therefore generically have extensive or "volume law" entanglement entropy at any non-zero temperature. They also generically obey the eigenstate thermalization hypothesis (ETH).