microcanonical ensemble - 2025 Penn Bowl

Question

In this model, the probability density of a particular allowed state is given by the reciprocal of the area of the phase space energy surface, which Aleksandr Khinchin called “fundamental distribution law.” For 10 points each:

[10h] Name this model used to describe the equilibrium probability distribution of closed, isolated systems.

ANSWER: microcanonical ensemble [accept NVE ensemble; reject “canonical ensemble”]

[10m] Khinchin’s “fundamental distribution law” also describes the time-average distributions of classical systems with this property. As a result, in systems with this property, all microstates are equally probable over time.

ANSWER: ergodic [accept ergodicity]

[10e] The ergodic hypothesis was formulated by this Austrian physicist, who also co-names the distribution followed by the canonical ensemble with Maxwell.

ANSWER: Ludwig Boltzmann [or Ludwig Eduard Boltzmann; accept Maxwell–Boltzmann distribution]

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Summary


2025 Penn Bowl - BU	11/01/25	Y	4	15.00	100%	50%	0%
2025 Penn Bowl - CWRU	11/01/25	Y	3	6.67	67%	0%	0%
2025 Penn Bowl - Mainsite (UPenn)	11/01/25	Y	6	8.33	83%	0%	0%
2025 Penn Bowl - Murray State	11/08/25	Y	2	10.00	100%	0%	0%
2025 Penn Bowl - Online	11/08/25	Y	2	10.00	100%	0%	0%
2025 Penn Bowl - Ottawa	11/01/25	Y	7	14.29	100%	43%	0%
2025 Penn Bowl - UK	11/01/25	Y	9	17.78	100%	44%	33%
2025 Penn Bowl - UNC	11/01/25	Y	3	13.33	100%	33%	0%
2025 Penn Bowl - WashU	11/01/25	Y	2	15.00	100%	50%	0%

Data


Brown	MIT A	0	10	10	20
I've been running into you in my lead plumbocene what could have benzene	Harvard	0	0	10	10
MIT B	Yale	0	0	10	10
RIT	Brandeis	0	10	10	20
Michigan B	Pittsburgh	0	0	0	0
Michigan A	Ohio State A	0	0	10	10
CWRU	Ohio State B	0	0	10	10
Maryland A	JHU B	0	0	10	10
Mount Sinai	Columbia A	0	0	10	10
JHU A	John Jay	0	0	10	10
Central Oklahoma	Texas B	0	0	10	10
Texas A	Oklahoma	0	0	10	10
New Young Whigs of America	abg academy	0	0	10	10
Wake Up Paddington A Washington Mystery	rusty shackleford	0	0	10	10
Maryland B	Swarthmore	0	0	10	10
Ottawa 67s	Aweille Kevin Fan osti continue comme ça	0	10	10	20
Toronto Operation PBSuccess	Guelph perfomative male competition	0	0	10	10
Waterloo you are crooked	McGill B	0	10	10	20
Toronto Murder on the Rider Express	McGill Fartlets	0	0	10	10
Queen's is monitoring the situation	Toronto E	0	0	10	10
Toronto G	Carleton A	0	10	10	20
#OpenToBuzz	Toronto Sunshine Bubbles	0	0	10	10
Maryland C	NYU B	0	0	0	0
Alas poor Warwick, I knew him Edinburgh	question mark	0	0	10	10
To buzz is to be perceived	Chimp Brisket	10	10	10	30
1. Wawa 2. Blank Street 151. Black Sheep at Kings Cross rail	Galactic Ombudsmen	0	0	10	10
Knorr Stock Clue	Penn and the Art of Tossup-Bonus cycle Maintenance	0	0	10	10
Hail to the Sheaf	Paul Quifford, or, It Was a Dark and Stormy Tournament	10	10	10	30
Quiztian Bale in Ratman Begins	Of Mice and Penn	0	0	10	10
The Bit and the Penndulum	Coughing Baby	0	10	10	20
Burnaburiash's Lapis Lazuli	Washed Scrubs	10	10	10	30
Bristold	why is it called a score clue if nobody scores points on it	0	0	10	10
Columbia B	NYU A	0	0	10	10
Planck Sinatra	Wise Duke	0	0	10	10
UNC A	UNC B	0	0	10	10
VT A	VT B	0	10	10	20
VJ Edgecombe School of Interior Design - Edwardsville	Truman State	0	0	10	10
WashU Kiki	WashU Bouba	0	10	10	20