We study the convergence of nonsymmetric annealing processes, extending the classical Dirichlet form approach to a broad class of Markov chains with exponentially vanishing transition functions. We show that both the true and symmetrized spectral gaps are logarithmically equivalent, and give robust estimates for the gap using geometric methods.
"$L^2$ Convergence of Time Nonhomogeneous Markov Processes: I. Spectral Estimates." Ann. Appl. Probab. 4 (4) 1012 - 1056, November, 1994. https://doi.org/10.1214/aoap/1177004901