Talk:Detailed balance

message: I'm pleased to see that there is now a discussion about the physical significance of detailed balance now.  But
I'm confused by the statement that the unitary nature of operators from quantum mechanics justifies our belief in
the reversibility of all physical processes.  Isn't this just replacing the assumption of detailed-balance with 
an assumption about a different set of matrices?  It seems to me that the second-law is best justified by our 
experiences and experiments.  —Preceding unsigned comment added by 146.186.131.40 (talk) 23:33, 15 February 2011 (UTC)
thread_title:  Physical Significance 

message: The current text says "Detailed balance is a weaker condition than requiring the transition matrix to be symmetric."  However, this is false, yes?  That is, a symmetric transition matrix need not represent a process with detailed balance.  As such neither condition is weaker than the other, right?  Quantling (talk) 19:16, 18 August 2010 (UTC)
replies: text: If you start with a uniform probability distribution, and apply a symmetric transition matrix to it, then at the next tick you will have the same distribution.  So this is a stationary state for the transition matrix.  By inspection, it clearly also obeys the equation for detailed balance.  Therefore it can indeed be said to be a stronger condition.  Jheald (talk) 19:37, 18 August 2010 (UTC)
thread_title:  Detailed balance is a weaker condition than requiring the transition matrix to be symmetric 

message: The current text says "The detailed balance condition is stronger than that required merely for a stationary distribution."  I think what is really meant is that detailed balance is not well defined unless the process is stationary.  For instance, if P_{ij} and \pi_i change with time, then at which time(s) do we evaluate the \pi_i, \pi_j, P_{ij}, and P_{ji} that appear in
:\pi_i P_{ij} = \pi_j P_{ji}\, ?
Can we change the text to remove the "stronger" language in favor of something that says that the concept of detailed balance makes sense only for a stationary process?  Quantling (talk) 19:44, 18 August 2010 (UTC)
replies: text: Although exhibiting detailed balance does not necessarily imply that a Markov process is a stationary process, it does necessarily imply that the Markov process has a stationary distribution.  My questions in this section reflect my confounding of these two "stationaries" and are thus somewhat nonsensical.  Please disregard them.  In the current text, I have partially reverted my edits, which had introduced stationary process where stationary distribution is appropriate.  —Quantling (talk) 16:42, 27 August 2010 (UTC)
thread_title:  The detailed balance condition is stronger than that required merely for a stationary distribution 

message: The article says that detailed balance is a "sufficient conditions for the strict increase of entropy in isolated systems". However, from my understanding detailed balance holding means that entropy stays constant because it implies the system is in equilibrium.  — Preceding unsigned comment added by Ryrythescienceguy (talk • contribs) 02:31, 15 May 2022 (UTC)
thread_title:  Detailed balance and entropy production