Black holes are one of the most mysterious concepts in physics and carry with them a large number of unsolved problems and counterintuitive results, none of which are more troubling than the information paradox.
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Traditional thermodynamics deals with macroscopic systems in thermal equilibrium, where one only has control over a few macroscopic variables (volume, temperature, etc).
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We give restrictions on locality-preserving unitary automorphisms U, which are protected gates, for 2-dimensional topologically ordered systems.
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