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Periodic thermodynamics of a two spin Rabi model

We consider two $s=1/2$ spins with Heisenberg coupling and a monochromatic, circularly polarized magnetic field acting only onto one of the two spins. This system turns out to be analytically solvable. Also the statistical distribution of the work performed by the driving forces during one period can be obtained in closed form and the Jarzynski equation can be checked. The mean value of this work, viewed as a function of the physical parameters, exhibits features that can be related to some kind of Rabi oscillation. Moreover, when coupled to a heat bath the two spin system will approach a non-equilibrium steady state (NESS) that can be calculated in the golden rule approximation. The occupation probabilities of the NESS are shown not to be of Boltzmann type, with the exception of a single phase with infinite quasitemperature. The parameter space of the two spin Rabi model can be decomposed into eight phase domains such that the NESS probabilities possess discontinuous derivatives at the phase boundaries. The latter property is shown to hold also for more general periodically driven $N$-level systems.