It is not easy to provide energy supply based on renewable energy enough to satisfy energy demand anytime and anywhere because the amount of renewable energy depends on geographical conditions and the time of day. In order to maximize the satisfaction of energy demand by renewable energy, surplus energy generated with renewable energy should be stored in batteries, and transmitted to electric loads with high demand somewhere in the electricity system. This paper proposes a novel autonomous decentralized mechanism of energy interchanges between distributed batteries on the basis of the diffusion equation and MCMC (Markov Chain Monte Carlo) for realizing energy supply appropriately for energy demand. Experimental results show that the proposed mechanism effectively works under several situations. Moreover, we discuss a method to easily estimate the behavior of the entire system by each node with the proposed mechanism, and the application potentiality of this estimating method to an efficient method working with non-renewable generators while minimizing the dependence of non-renewable energy, and an incentive mechanism to prevent monopolizing energy in systems.