Balance Equation - Detailed Balance

Detailed Balance

See also: Detailed balance

For a continuous time Markov chain (CTMC) with transition rate matrix Q, if can be found such that for every pair of states i and j

holds, then the global balance equations are satisfied and is the stationary distribution of the process. If such a solution can be found the resulting equations are usually much easier than directly solving the global balance equations.

A CTMC is reversible if and only if the detailed balance conditions are satisfied for every pair of states i and j.

A discrete time Markov chains with transition matrix P and equilibrium distribution is said to be in detailed balance if for all pairs i and j,

When a solution can be found, as in the case of a CTMC, the computation is usually much quicker than directly solving.

Read more about this topic:  Balance Equation

Other articles related to "detailed balance, detailed":

Detailed Balance For Systems With Irreversible Reactions
... Detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process and required reversibility of all elementary processes ... catalytic oxidation, most enzyme reactions etc.), detailed mechanisms include both reversible and irreversible reactions ... with irreversible reactions can be obtained as limits of systems or reversible reactions with detailed balance ...
Quantum Superposition - Theory - Quantum Mechanics in Imaginary Time
... In probability theory, the probability m for the stochastic matrix obeys detailed balance when the stationary distribution has the property Detailed balance says that the ... form when written as a condition for the transition-probability R matrix When the R matrix obeys detailed balance, the scale of the probabilities can be redefined ...
Microscopic Reversibility - Macroscopic Consequences of The Time-reversibility of Dynamics
... the time-reversibility of microscopic dynamics the principle of detailed balance and the Onsager reciprocal relations ... that the time-reversibility of the Newtonian dynamics leads to the detailed balance for collision in equilibrium collisions are equilibrated by their reverse collisions ... He found also the connection between the reciprocal relations and detailed balance ...

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