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