Bonus
The fact that the set of Gibbs measure has this property means that a system either has a unique Gibbs measure or infinitely many. For 10 points each:
[10h] Name this property that thermodynamic potentials must have with respect to their [emphasize] extensive variables by the thermodynamic stability criterion.
ANSWER: convexity [accept concave up; reject “concave”]
[10m] A unique Gibbs measure corresponds to a statistical mechanical system having this property. In thermodynamic systems with this property, time averages equal ensemble averages according to a namesake theorem.
ANSWER: ergodic [or ergodicity; accept unique ergodicity or uniquely ergodic or ergodic theorems]
[10e] The existence of more than one Gibbs measure can indicate one of these events. Freezing is a first-order example of one of these events.
ANSWER: phase transitions [or phase changes or phase transformations; accept first or second order phase transitions]
<Physics>
Answerlines and category may not exactly match the version played at all sites
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Columbia A | Minnesota | 0 | 10 | 10 | 20 | ME |
Summary
| Tournament | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| 2025 ACF Nationals | Yes | 1 | 20.00 | 100% | 100% | 0% |