The discussion centers on the concept of microstates in statistical mechanics, specifically addressing what determines the maximum number of microstates at equilibrium for two non-interacting systems with different energy levels. The focus is on understanding the product of microstates and its implications for total states in a system.
Participants generally agree on the interpretation of the product of microstates for non-interacting systems, but there is a lack of consensus on the deeper implications of this relationship at equilibrium, as some questions remain unanswered.
The discussion does not fully explore the assumptions behind the definitions of microstates or the conditions under which the product holds, leaving some aspects unresolved.
Apologies if the answer is obvious, but why does ## \Omega(E_1)\Omega(E_2) ## give the total number of states?Lord Jestocost said:Such a product term means the total number of states
##\Omega(E_1,E_2)=\Omega(E_1)\Omega(E_2)##
of two non-interacting systems with energies ##E_1## and ##E_2##, respectively.
Ah of course. Thanks, that cleared things up.Nugatory said:The first system may be in any of ##\Omega(E_1)## states; for any of these the second may be in any of ##\Omega(E_2)## states. It’s really no different than a system of consisting of two standard six-sided dice: the first may be in any of six states, the second may be in any of six states, so there are six times six equals thirty-six possible states for the two-dice system.