The optimization of a randomness extractor can be best determined from the “min” variant of this variable as the smallest of the Rényi family variants of this variable. For a uniform probability distribution the Hartley function is equivalent to one definition of this variable. A quantum type of this variable vanishes when the density matrix is that of a pure state and is named for (*) Von Neumann. The molecular chaos assumption was used to derive an integral equal to a function of this variable, which following later convention was represented with an H. Gibbs created a definition of this variable based on a summation of a function of the probability of microstate energies. For 10 points, name this variable equal to the Boltzmann constant times the natural log of microstates. ■END■
| 2025 Penn Bowl - Stanford | 10/25/25 | Y | 4 | 100% | 50% | 0% | 61.50 |
| 2025 Penn Bowl - Northwestern | 10/25/25 | Y | 4 | 100% | 25% | 0% | 74.00 |
| 2025 Penn Bowl - Mainsite (UPenn) | 11/01/25 | Y | 6 | 100% | 0% | 0% | 99.50 |
| 2025 Penn Bowl - BU | 11/01/25 | Y | 4 | 100% | 25% | 0% | 69.25 |
| 2025 Penn Bowl - CWRU | 11/01/25 | Y | 3 | 100% | 0% | 0% | 104.67 |
| 2025 Penn Bowl - UNC | 11/01/25 | Y | 3 | 100% | 0% | 0% | 117.67 |
| 2025 Penn Bowl - WashU | 11/01/25 | Y | 2 | 100% | 0% | 0% | 110.00 |
| 2025 Penn Bowl - Ottawa | 11/01/25 | Y | 7 | 100% | 29% | 0% | 74.71 |
| 2025 Penn Bowl - UK | 11/01/25 | Y | 9 | 100% | 33% | 0% | 68.44 |
| 2025 Penn Bowl - Online | 11/08/25 | Y | 2 | 100% | 0% | 0% | 73.00 |
| 2025 Penn Bowl - Murray State | 11/08/25 | Y | 2 | 100% | 0% | 0% | 81.00 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Nathan Sheffield | MIT A | RIT | 21 | 15 |
| Matt Booth | Burnaburiash's Lapis Lazuli | why is it called a score clue if nobody scores points on it | 27 | 15 |
| Asha Basu | McGill B | Toronto G | 27 | 15 |
| Linus Luu | question mark | Washed Scrubs | 31 | 15 |
| Colin Veevers | Ottawa 67s | Toronto Operation PBSuccess | 32 | 15 |
| Adil Soubki | Galactic Ombudsmen | Coughing Baby | 43 | 15 |
| Alex Akridge | Indiana | Purdue A | 43 | 15 |
| Danny Han | Stanford B | Berkeley C | 56 | 15 |
| Aditya Patnaik | Ohio State A | Ohio State B | 57 | 10 |
| Daniel Hothem | In Search of Lost Clues | Berkeley A | 58 | 15 |
| Joy An | Harvard | MIT B | 66 | 10 |
| Caleb Ott | Waterloo you are crooked | Toronto E | 66 | 10 |
| Shahar Schwartz | Free Win | Berkeley B | 66 | 10 |
| Richard Niu | The best time to buzz was twenty clues ago. The second best time to buzz is now | Stanford A | 66 | 10 |
| Vivek Sasse | Hail to the Sheaf | 1. Wawa 2. Blank Street 151. Black Sheep at Kings Cross rail | 66 | 10 |
| Omer Keskin | Penn and the Art of Tossup-Bonus cycle Maintenance | Quiztian Bale in Ratman Begins | 66 | 10 |
| Joseph Krol | To buzz is to be perceived | Alas poor Warwick, I knew him Edinburgh | 66 | 10 |
| Will Alston | rusty shackleford | abg academy | 66 | 10 |
| Mattias Ehatamm | Maryland A | Columbia B | 66 | 10 |
| Matthew He | Texas B | Oklahoma | 66 | 10 |
| Beckett Pursey | Purdue B | UChicago C | 67 | 10 |
| Denali Tran-Le | McGill Fartlets | Carleton A | 68 | 10 |
| Ryan Rosenberg | NYU A | JHU B | 68 | 10 |
| Ezra Santos | UChicago A | UChicago B | 69 | 10 |
| Mason Yu | Brown | I've been running into you in my lead plumbocene what could have benzene | 72 | 10 |
| Braxton Davis | New Young Whigs of America | Wake Up Paddington A Washington Mystery | 80 | 10 |
| Aneesh Swaminathan | JHU A | NYU B | 92 | 10 |
| Logan Mathis | WashU Kiki | Truman State | 93 | 10 |
| Collin Leck | Central Oklahoma | Texas A | 96 | 10 |
| Imran Rahman | Chimp Brisket | Bristold | 99 | 10 |
| Kais Jessa | Aweille Kevin Fan osti continue comme ça | Toronto Sunshine Bubbles | 103 | 10 |
| Kai Madgwick | Knorr Stock Clue | The Bit and the Penndulum | 106 | 10 |
| Aditya Sharma | Wise Duke | Planck Sinatra | 111 | 10 |
| Jacob Bicol | #OpenToBuzz | Queen's is monitoring the situation | 112 | 10 |
| Ethan Webb | Of Mice and Penn | Paul Quifford, or, It Was a Dark and Stormy Tournament | 112 | 10 |
| Nick Smemoe | UNC A | UNC B | 112 | 10 |
| Moses Kitakule | Columbia A | Maryland B | 112 | 10 |
| Rayton Lin | Guelph perfomative male competition | Toronto Murder on the Rider Express | 115 | 10 |
| Andrew Wang | Illinois | Northwestern B | 117 | 10 |
| Nathaniel Martin | Brandeis | Yale | 118 | 10 |
| Ariel Faeder | Pittsburgh | Michigan B | 127 | 10 |
| Neal Joshi | VJ Edgecombe School of Interior Design - Edwardsville | WashU Bouba | 127 | 10 |
| Ben Hellman | Swarthmore | Mount Sinai | 129 | 10 |
| Aryan Desarapu | Michigan A | Michigan C | 130 | 10 |
| Thomas Glotfelty | VT A | VT B | 130 | 10 |
| Jerry Vinokurov | John Jay | Maryland C | 130 | 10 |