We consider strong two-body losses in bosonic gases trapped in one-dimensional optical lattices. We exploit the separation of timescales typical of a system in the many-body quantum Zeno regime to establish a connection with the theory of the time-dependent generalized Gibbs ensemble. Our main result is a simple set of rate equations that capture the simultaneous action of coherent evolution and two-body losses. This treatment gives an accurate description of the dynamics of a gas prepared in a Mott insulating state and shows that its long-time behavior deviates significantly from mean-field analyses. The possibility of observing our predictions in an experiment with ${}^{174}\mathrm{Yb}$ in a metastable state is also discussed.

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• Decoherence in quantum gases
• Eigenstate thermalization
• Quantum Zeno dynamics
• Quantum master equation
• 1-dimensional systems
• Perturbative methods