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Given a many-body system, we define a quantity, the Codification Volume of anoperator algebra, which measures the size of the subspace with whom a givenalgebra is correlated. We explicitly calculate it for some limit cases,including vacuum states of local Hamiltonians and random states taken from theHaar ensemble. We argue that this volume should grow irreversibly in athermalization process, and illustrate it numerically on a non-integrablequantum spin chain.

Codification Volume of an operator algebra and its irreversible growth through thermal processes