Reversible Dynamics - Stochastic Processes

Stochastic Processes

A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process. More formally, for all sets of time increments { τs }, where s = 1..k for any k, the joint probabilities

p(x_t, x_{t+\tau_{1}}, x_{t+\tau_{2}} .. x_{t+\tau_{k}}) = p(x_{t'}, x_{t'-\tau_{1}}, x_{t'-\tau_{2}} .. x_{t'-\tau_{k}})

A simple consequence for Markov processes is that they can only be reversible if their stationary distributions have the property

This is called the property of detailed balance.

Read more about this topic:  Reversible Dynamics

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