Exponential convergence of fisher entropy for diffusion processes

In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in R ^d and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry-Emery condition.