A remark on rapid mixing for hyperbolic flows

In this short paper, we introduce a new criterion based on the temporal distance function that guarantees rapid mixing for a hyperbolic flow with respect to Gibbs measures. This criterion is probabilistically satisfied almost surely but lacks robustness. Moreover, it enables us to establish rapid mixing for a class of hyperbolic flows that do not meet the existing rapid mixing criteria. Furthermore, beyond uniform hyperbolicity, our proof also works for a significant category of non-uniformly hyperbolic flows that can be modeled by Young towers.