Entropy dissipation for some non-reversible stochastic differential equations

We formulate explicit bounds to guarantee the exponential dissipation for some non-gradient stochastic differential equations towards their invariant distributions. We apply Lyapunov methods in the space of probabilities, where the Lyapunov functional is chosen as the relative Fisher information between current density and invariant distribution. We derive the Fisher information induced Gamma calculus to handle non-gradient drift vector fields. From it, we obtain the explicit dissipation bound in terms of L1 distance. An analytical example is provided for a non-reversible Langevin dynamic.