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Abstract This study examines the variability of tropical cyclone (TC) intensity associated with stochastic forcings at the maximum potential intensity (PI) equilibrium. By representing TC intensity as an Itô diffusion process in the framework of TC-scale dynamics, we show from both theoretical and numerical analyses that there exists an invariant intensity distribution whose variance is proportional to the variances of stochastic forcings. This result provides further evidence that TC dynamics possess an intrinsic variability that prevents the TC absolute intensity errors in numerical models from being reduced below an arbitrarily small threshold. Analysis of the invariant intensity distribution at the PI limit reveals also that the stochastic forcing component associated with tangential wind and the warm-core anomaly in the TC central region have the largest contribution to TC intensity variability. These results suggest that future development of stochastic representation in TC models should focus on the tangential wind and thermodynamic structure to capture proper TC intensity random fluctuations.