# Detailed Balance: meaning?

1. May 28, 2010

### M.B.

Hey,

I was wondering in what way the detailed balance condition (DBC) has to do with thermodynamic equilibrium.

The DBC is defined as
$$W(i\to j)P(i) = W(j\to i)P(j)$$
with W the rates (probabilities per unit time) to jump from state i to j. P(i) is the equilibrium prob. density to have state i, this could be e.g. a Boltzmann Gibbs distribution in case of canonical equilibrium.
When for a (Markov jump) proces the above equality holds, then the system is time-reversible: it is even likely to follow a path forward in time or backwards in time

My question is:
The above formula is always possible to write down, but how is this related to equilibruim?

2. Jun 1, 2010