  In this paper a class of dynamical systems describing expectation variables
exactly derived from continuous-time master equations is introduced and studied
from the viewpoint of differential geometry, where such master equations
consist of a set of appropriately chosen Markov kernels. To geometrize such
dynamical systems for expectation variables, information geometry is used for
expressing equilibrium states, and contact geometry is used for nonequilibrium
states. Here time-developments of the expectation variables are identified with
contact Hamiltonian vector fields on a contact manifold. Also, it is shown that
the convergence rate of this dynamical system is exponential. Duality
emphasized in information geometry is also addressed throughout.
