This paper analyses the properties of the continuous Time Markov Chains using circulation theory. Applying the Hill's circulation theory on Markov chains, the Steady state probabilities of the Markov chains are calculated. The dynamics of ecological systems can be conveniently described as a Markovian stochastic process. Entropy production can successfully characterize ecological systems with cyclic competition. Ecological systems display a wide variety of nonlinear and non equilibrium behavior. Random interactions between individuals and the finiteness of the population lead to intrinsic stochasticity. Nonequilibrium results when interactions between individuals of different species include cyclic dependencies. This paper analyzes the Entropy production in terms of Markovian Steady State Probabilities.