The partition function for state 1: RNA polymerase molecules (P) to bind to nonspecific sites (NNS) (one molecule per site):
The partition function for state 2: one RNA polymerase molecule to bind to the promoter (equivalent to P-1 RNA polymerase molecules bound to NNS nonspecific sites AND one on promoter):
The total partition function for the p RNA polymerase molecules when they are bound to nonspecific or promoter sites:
The total number of states available to the combined universe of system and reservoir when the system is in a particular microstate with energy Es(1) is:
The probability for finding the system in state i with energy Es(i) is (Boltzmann distribution): (With the partition function)
The probability of the macrostate X equation (include State, Weight chart):
G(X)=? (In terms of Entropy & simplification of W, p(X)=?):
Boltzmann distribution in terms of total energy to be shared among N particles:
The entropy of ideal gas reflects the freedom to rearrange....
The entropy of ideal gas reflects the freedom to rearrange both molecular positions and velocities (energy)
For the momentum in x direction px, the contribution to the kinetic energy is:
Using the Boltzmann distribution for a system with energy Ei:
Average energy of a molecule in gas expressed in terms of momentum:
Converting Average energy of a molecule in gas into continuous variable: