Question
Schnakenberg network theory is used to graphically analyze this class of equations, which are often used to describe small systems transitioning between coarse-grained configurations. For 10 points each:
[10h] Name this class of equations that describe the time evolution of the probability of a set of states, exemplified by the equation dp-dt equals R-hat p. The Lindblad equation is a quantum Markovian one of these equations.
ANSWER: master equations [accept quantum master equation]
[10e] Steady-state solutions to the master equation that additionally satisfy detailed balance are in this physical state. A thermodynamic system in this state exhibits no macroscopic flows of energy or matter.
ANSWER: thermodynamic equilibrium
[10m] When the number of states is large, the master equation can be simulated by sampling trajectories using the “kinetic” form of this method. These methods estimate integrals by averaging over samples taken from a complex probability distribution.
ANSWER: Monte Carlo [accept kinetic Monte Carlo or KMC; accept MCMC or Markov chain Monte Carlo; prompt on MC]
<Physics>
Summary
| 2024 ACF Regionals @ Berkeley | 01/27/2024 | Y | 3 | 13.33 | 67% | 67% | 0% |
| 2024 ACF Regionals @ Cornell | 01/27/2024 | Y | 2 | 10.00 | 100% | 0% | 0% |
| 2024 ACF Regionals @ JMU | 01/27/2024 | Y | 4 | 10.00 | 75% | 0% | 25% |
| 2024 ACF Regionals @ Minnesota | 01/27/2024 | Y | 2 | 10.00 | 100% | 0% | 0% |
| 2024 ACF Regionals @ Nebraska | 01/27/2024 | Y | 1 | 10.00 | 100% | 0% | 0% |
| 2024 ACF Regionals @ Rutgers | 01/27/2024 | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 1 | 10.00 | 100% | 0% | 0% |
Data
| Stanford C | Berkeley C | 0 | 0 | 0 | 0 |
| Stanford B | Berkeley B | 0 | 10 | 10 | 20 |
| Stanford A | Berkeley A | 0 | 10 | 10 | 20 |