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We prove fundamental rigorous bounds on the speed of quantum evolution for aquantum system coupled to a thermal bath. The bounds are formulated in terms ofexpectation values of few-body observables derived from the system-bathHamiltonian. They do not rely on the Markov approximation and, as aconsequence, are applicable beyond the limit of weak system-bath coupling.

Quantum speed limits for an open system in contact with a thermal bath