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Collective versus individual classicality for a pair of interacting qubits immersed in independent local environments

There is current interest in investigating which variables play an important role in the physical processes with an open composite quan- tum system that ranges from the foundational issues to the tasks of diverse applications in quantum physics and technology. In this paper we contrast the local versus the collective classical-like behavior of a pair of interacting qubits immersed in the mutually independent thermal baths. The qubits can be locally subjected to any of the standard, microscopically modelled, generalized amplitude damping and phase damping channel, as well as to the recently introduced generalized depolarizing channel. As a criterion for the classical-like behavior we use the least entropy production, i.e. the total correlation in the system. The classical-like collective behavior is found for short time intervals for strongly interacting qubits. Only in a certain trivial case we observe the simultaneous collective and individual-qubits classical- ity. Observation (non-observation) of the collective (individual) classicality can reveal the kind and strength of the qubits interaction or the ratio of the qubits' energy-gaps, while manipulating the qubits interaction (by tuning the strength and/or refocussing) can give rise to the desired kind of classicality.