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Two macroscopic states A and B. Suppose S(A)>S(B). What can we say about probabilities?
All microscopic states in microcanonical ensemble are equal. Probability is proportional to the number of states.
The state with greater entropy is more probable
Thermodynamic limit: , ,
In thermodynamic limit we can see only the states with maximal entropy .
Equations of mechanics are time reversible . How can irreversibility appear in the picture?
Glass falls from a table an is broken. All molecular motions are reversible. What about irreversibility??
Happy families are all alike; every unhappy family is unhappy in its own way.
We discussed systems that do not move. What happens if it moves with the velocity v?
Entropy depends only on the internal energy:
What happens if a system separates into two parts that move apart?
If T<0, entropy increases --the process is favorable. Systems with negative temperatures would want to blast off!
In fully equilibrated systems T>0. But partially equilibrated systems might have negative T for some degrees of freedom.
© 1997 Boris Veytsman and Michael Kotelyanskii