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We formulate explicit bounds to guarantee the exponential dissipation forsome non-gradient stochastic differential equations towards their invariantdistributions. Our method extends the connection between Gamma calculus andHessian operators in $L^2$--Wasserstein space. In details, we apply Lyapunovmethods in the space of probabilities, where the Lyapunov functional is chosenas the relative Fisher information. We derive the Fisher information inducedGamma calculus to handle non-gradient drift vector fields. We obtain theexplicit dissipation bound in terms of $L_1$ distance and formulate thenon-reversible Poincar{\'e} inequality. An analytical example is provided for anon-reversible Langevin dynamic.

Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equations