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Dynamics and features of quantum systems may be drastically different from classical systems. Dissipation is generally understood as a general mechanism through which quantum systems may lose part or all of their quantum aspects. Here we discuss a method to analyze behaviors of dissipative quantum systems in an algebraic
sense. This method employs a time-dependent product between systems observable which is induced by the underlying dissipative dynamics. We argue that the longtime limit of the algebra of observables defined with this product yields a contractive algebra, which reflects the loss of some quantum features of the dissipative system and bears relevant information about irreversibility. We illustrate this result through
several examples of dissipation in various Markovian and non-Markovian systems
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