Question
Integrals over the Fermi–Dirac and Bose–Einstein distributions define a “poly” form of this function. The replica trick takes advantage of the fact that this function of Z is equal to the limit as n approaches zero of “Z-to-the-n, minus one, all over n.” The expected value of the energy is equal to the negative partial derivative of this function of Z with respect to beta. The Helmholtz free energy is equal to kT times this function of the partition function. Stirling’s formula approximates this function of n-factorial. The negative sum over all states of “p times this function of p” defines the Shannon entropy, while Boltzmann’s definition of entropy is equal to k times this function of the number of microstates. For 10 points, name this function, the inverse of the exponential function. ■END■
Summary
2024 ACF Regionals @ Berkeley | 01/27/2024 | Y | 3 | 100% | 0% | 33% | 59.00 |
2024 ACF Regionals @ Cornell | 01/27/2024 | Y | 3 | 100% | 0% | 67% | 92.67 |
2024 ACF Regionals @ JMU | 01/27/2024 | Y | 10 | 90% | 0% | 10% | 108.00 |
2024 ACF Regionals @ Nebraska | 01/27/2024 | Y | 6 | 100% | 0% | 33% | 110.67 |
2024 ACF Regionals @ Ohio State | 01/27/2024 | Y | 3 | 100% | 0% | 33% | 117.33 |
2024 ACF Regionals @ Rutgers | 01/27/2024 | Y | 5 | 100% | 0% | 40% | 86.60 |
2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 8 | 88% | 0% | 75% | 115.71 |
2024 ACF Regionals @ Vanderbilt | 01/27/2024 | Y | 5 | 100% | 0% | 60% | 121.00 |
Buzzes
Player | Team | Opponent | Buzz Position | Value |
---|---|---|---|---|
Rasheeq Azad (UG) | UNC B (UG) | Duke A (UG) | 24 | 10 |
Kenny Zhang (UG) | Virginia A (UG) | GWU B (Grad) | 82 | -5 |
Jim Fan (Grad) | UNC A (Grad) | Maryland B (UG) | 86 | 10 |
Isaac Mammel (UG) | Maryland A (Grad) | JMU B (UG) | 88 | 10 |
Brian Lai (DII) | Virginia B (UG) | UNC D (DII) | 110 | 10 |
Perry O'Connor (Grad) | Liberty A (Grad) | Liberty C (DII) | 132 | 10 |
Kevin Liu (DII) | Maryland C (DII) | GWU A (UG) | 133 | 10 |
Carly Hemani (DII) | JMU A (UG) | Roanoke College A (DII) | 133 | 10 |
Michael Eng (UG) | UNC C (UG) | Liberty B (DII) | 133 | 10 |
Annie Goodman (Grad) | GWU B (Grad) | Virginia A (UG) | 133 | 0 |
Zander Werner (DII) | Virginia C (UG) | William & Mary A (UG) | 133 | 10 |