In this lecture, we continue our march toward Simulated Annealing by ensuring that we have the necessary foundations in information theory to support discussing thermodynamics and statistical mechanics. This allows us to introduce Boltzmann sampling, which will be used in Simulated Annealing, and the computational applications from physical chemistry that first inspired the creation of Boltzmann sampling. In particular, we introduce Monte Carlo integration and start to discuss how Boltzmann sampling can greatly reduce the number of samples necessary to estimate macroscopic variables of interest to physicists as they investigate thermodynamic equations of state. This also effectively allows us to introduce Markov Chain Monte Carlo (MCMC) methods, of which the Metropolis algorithm is recognized as the first popular MCMC method (and the foundation of Simulated Annealing).
Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/0nmyk60h6xtfa335x2bpd/IEE598-Lecture5C-2025-03-25-Toward_Simulated_Annealing-Introduction_to_Boltzmann_sampling_and_Monte_Carlo_integration-Notes.pdf?rlkey=ig1tbmmyenqpt7b6vwtnzbkem&dl=0
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