- #1

Ted Ali

- 12

- 1

- Homework Statement
- Consider the grand canonical ensemble, for a system A with N identical particles. This system can exchange particles with a reservoir A'. We consider only small deviations from equilibrium. What is the necessary and sufficient condition that the Lagrange multiplier ##\alpha## of N, must satisfy?

- Relevant Equations
- The Lagrange multiplier ##\alpha## is: $$\alpha =\left( \frac{\partial \ln \Omega}{\partial N'} \right)$$.

According to the book "Principles of Statistical Mechanics" by Amnon Katz, page 123, ##\alpha## must be such that ##\exp ( -\alpha N ) ## can be expanded in powers of ##\alpha## with only the first order term kept. Is this the necessary and sufficient condition for small deviations from equilibrium?

Thank you in advance,

Ted.

Thank you in advance,

Ted.