- #1

Kashmir

- 468

- 74

"... two physical systems [seperated by wall], A1 and A2. A1 has ##\Omega_{1}(N1,V1,E1)## possible microstates, and the macrostate of A2 is ##\Omega_{2}(N2,V2,E2)## "

"... at any time ##t##, the subsystem ##A_{1}## is equally likely to be in anyone of the ##\Omega_{1}\left(E_{1}\right)## microstates while the subsystem ##A_{2}## is equally likely to be in anyone of the ##\Omega_{2}\left(E_{2}\right)## microstates; therefore, the composite system ##A^{(0)}## is equally likely to be in anyone of the

##

\Omega_{1}\left(E_{1}\right) \Omega_{2}\left(E_{2}\right)=\Omega_{1}\left(E_{1}\right) \Omega_{2}\left(E^{(0)}-E_{1}\right)=\Omega^{(0)}\left(E^{(0)}, E_{1}\right)

##"

"... if A1 and A2 came into contact through a wall that allowed an exchange of particles as well, the conditions for equilibrium would [include] the equality of the parameter ##\zeta_{1}## of subsystem ##A_{1}## and the parameter ##\zeta_{2}## of subsystem ##A_{2}## where, by definition,

##

\zeta \equiv\left(\frac{\partial \ln \Omega(N, V, E)}{\partial N}\right)_{V, E, N=\bar{N}}

##"

• So if we've a wall that allowed an exchange of particles we have from above equation:

##

\left(\frac{\partial \ln \Omega_1(N_1, V_1, E_1)}{\partial N_1}\right)_{V_1, E_1, N=\bar{N}}

=\left(\frac{\partial \ln \Omega_2(N_2, V_2, E_2)}{\partial N_2}\right)_{V_2, E_2, N=\bar{N}}

##

However having a wall that allows particles to be exchanged means no wall at all, then ##V_1,V_2## are not well defined, but the above equation uses them?