Section 12. Thermodynamic Description

12.3 Kadanoff’s angels

In 1980 Leo Kadanoff gave a graduate course on nonequilibrium statistical mechanics at University of Chicago. He almost avoided any discussion on the ‘origin’ of irreversibility from mechanics. He mentioned some meeting devoted to this topic and commented roughly as: They discussed how many angels could sit on a pinhead. 

12.10 Why is thermodynamics useful?

 The verdicts or thermodynamics do not allow any exception;they are absolute. 

(1) If thermodynamics forbids a process, it is never possible.

(2) If no thermodynamic principles conclude a process is forbidden, then there must be a way to realize it.

 Suppose there are two processes for which entropy changes satisfy the following 

 inequalities:

 In this case, there must be a way to couple the two processes to realize the `miracle, ie., 

 the first process, using the second process to drive it. Needless to say, actually devising 

 the needed coupling may well be highly nontrivial, but we can say that life is sustained 

 by such coupled processes. That is why may processes look miraculous.

(3) If thermodynamics cannot predict a unique final state, then extrathermodynamic conditions are needed to determine the destination of the process.