Detailed Balance

The concept of detailed balance ( engl. detailed balance ) refers to a property of homogeneous Markov chains. It means that the probability of a state at equilibrium ( ) multiplied by the transition probability from state to state ( ) is equal to the probability of a state () in equilibrium multiplied by the transition probability from state to state ( ) is:

For stationary Markov chain with transition matrix, this property is equivalent to the temporal reversibility, that is, for the time-reversed process applies to all

These processes can be used to to bring systems from suitable initial states in the canonical equilibrium:

Reversible Markov processes fulfill the requirement to bring states to the canonical equilibrium, but are not a necessary prerequisite.

The Metropolis algorithm is an example of a stochastic process that satisfies the property of Detailed Balance. It is used in Monte Carlo simulations to generate states of a system from previous states according to a transition probability.