Round 6: Tossup 11

This quantity characteristically scales logarithmically with evolution time in systems displaying many-body localization. This quantity evolves over time to form an inverted V shape on the Page curve. For a tripartite quantum system, this quantity obeys strong subadditivity. (10[1])For pure states, (10[1])the distillable and squashed entanglements reduce to this quantity. For a system with density matrix rho, this quantity equals the negative trace of rho times log rho. By the (10[1])Bekenstein–Hawking (10[1])formula, the area of a black hole is proportional to its value of this quantity. (10[1])In classical information theory, this quantity expresses the absence of information about a system (10[1])and is measured in shannons. (10[1])For 10 points, name this quantity that increases in accordance with the second law of thermodynamics. (10[1])■END■

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