The Canonical Assembly

The assembly that results from these conditions is called the canonical assembly Let us formulate the conditions which it must satisfy. It 

This quantity must be held constant in varying the/t s. Also, as we saw in Eq. (1.1), the quantity equals unity. This must always be satis- 

The set of simultaneous equations (5.3), (5.4), (5.5) can be handled by the method called undetermined multipliers the most general value which ln/ can have, in order that dS should be zero for any set of dfi s for which Eqs. (5.3) and (5.4) are satisfied, is a linear combination of the coefficients of dfi in Eqs. (5.3) and (5.4), with arbitrary coefficients  

Clearly b must be negative for ordinary systems have possible states of infinite energy, though not of negatively infinite energy, and if b were positive, would become infinite for the states of infinite energy, an impossible situation. We may easily evaluate the constant a in terms of 

If the assembly (5.9) represents thermal equilibrium, the change of entropy when a certain amount of heat is absorbed in a reversible process 

---

There are two basic approaches to the computer simulation of liquid crystals, the Monte Carlo method and the method known as molecular dynamics. We will first discuss the basis of the Monte Carlo method. As is the case with both these methods, a small number (of the order hundreds) of molecules is considered and the difficulties introduced by this restriction are, at least in part, removed by the use of artful boundary conditions which will be discussed below. This relatively small assembly of molecules is treated by a method based on the canonical partition function approach. That is to say, the energy which appears in the Boltzman factor is the total energy of the assembly and such factors are assumed summed over an ensemble of assemblies. The summation ranges over all the coordinates and momenta which describe the assemblies. As a classical approach is taken to the problem, the summation is replaced by an integration over all these coordinates though, in the final computation, a return to a summation has to be made. If one wishes to find the probable value of some particular physical quantity, A, which is a function of the coordinates just referred to, then statistical mechanics teaches that this quantity is given by... 

Exercise 6.3. Improve the user friendliness of fig6-5.xls by assembling all the primary data of interest on the CANONICAL worksheet. 

---