  We analyze the entropy behavior of the de Sitter spacetime during the
inflationary phase. A cosmological horizon in de Sitter spacetime that
constrains the causally accessible region of an observer exhibits thermal
properties analogous to the event horizon of a black hole. According to the
principles of holography, the entropy within a causally connected region for an
observer is limited by its boundary. This entropy bound is violated during the
late inflation stage. To address the issue of entropy bound violations from a
quantum information perspective, we adopted a stochastic approach to cosmic
inflation. We consider Shannon entropy of the probability distribution of the
inflaton field, which shows the same behavior as the entanglement entropy of a
Hubble-size region in stochastic inflation. Adopting the volume-weighted
probability distribution for the inflaton field, we show a meaningful entropy
behavior in the de Sitter spacetime.
