Generalized second law of thermodynamics and cosmological decoherence

We point out that the generalized second law of thermodynamics on a de Sitter universe whose energy density stochastically fluctuates due to quantum fluctuations is seemingly violated. We show that, even in such a case, the generalized second law is unviolated by taking cosmological decoherence into account. It is well known that the decoherence is necessary to reasonably explain why our Universe looks classical. Our proposal can support the importance of decoherence from another aspect, i.e., the generalized second law of thermodynamics.