1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Detailed Balance: meaning?

  1. May 28, 2010 #1

    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. jcsd
  3. Jun 1, 2010 #2
    It is obvious that the probability distribution must not change by the flows. So you see that your equation states that the same amount of thingamajigs are jumping from i to j as from j to i. Hence the distribution stays the same under time evolution. If you know W then you can derive an equilibrium distribution with the DBC.

    If the DBC holds than P is an equilibrium distribution. I am not sure if the inverse direction is also true.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook