Packet 3: Bonus 19

Applying the mean-field approximation produces an upper bound on this quantity via the Bogoliubov inequality. For 10 points each:
[10m] Name this quantity from which chemical potential times particle number is subtracted to obtain the grand potential. This thermodynamic potential has natural variables of temperature and volume.
ANSWER: Helmholtz free energy [prompt on free energy]
[10e] The grand potential is the state function for the “grand canonical” type of these systems, which in statistical mechanics are large collections of particles that encode all possible microstates.
ANSWER: statistical ensembles [accept thermodynamic ensembles; accept grand canonical ensemble]
[10h] The grand potential is sometimes used instead of Helmholtz free energy in these models that construct an order parameter at an interface. The Cahn–Hilliard and Allen–Cahn equations are used for these models depending on whether the interface is sharp or diffuse.
ANSWER: phase-field models [or phase-field methods]
<Editors, Physics> | L. Playoffs 3 (Editors 3)

HeardPPBE %M %H %
1016.00100%60%0%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Chicago AVirginia Tech1010020ME
Columbia BVirginia010010E
GeorgetownPurdue010010E
HarvardNorthwestern A1010020ME
TexasGeorgia Tech C010010E
Toronto ANYU A1010020ME
Toronto BPittsburgh010010E
UC Berkeley AIndiana1010020ME
UC Berkeley BColumbia A1010020ME
WaterlooNorth Carolina1010020ME

Summary

TournamentEditionMatchHeardPPBE %M %H %
Main Site2026-04-17✓1016.00100%60%0%