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We consider thermalization of a microscopic quantum system by interactionwith a thermal bath. Our interest is the minimal size the bath can have whilestill being able to thermalize the system. Within a specific thermalizationscheme we show that a single spin-1/2 can be fully thermalized by interactionwith a bath that consists of just two other spin-1/2. The two bath spins areinitially in a pure, entangled state, and the thermalizing interaction is aHeisenberg exchange-interaction of the system-spin with one of the bath spins.The time dependent coupling strength has to obey a single integral constraint.We also present a simple generalization of this minimal model in which the bathconsists of an arbitrary number of spin-1/2 pairs.

How two spins can thermalize a third spin