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In a desperate attempt to preserve my own sanity, a survey of probability distributions used to describe a single, continuous, unimodal, univariate random variable.
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People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.
This was a fun paper that originated in a chance, serendipitous conversation between myself, Jerome and John. We realized that several different Monte Carlo sampling techniques that we had each recently worked on could be unified under a common framework by taking inspiration from nonequilibrium thermodynamics. (I am also particularly satisfied with the joke. I firmly believe every scientific paper should contain one joke, lest we take ourselves too seriously. This one is great because it’s hiding in plain sight.)
Abstract: Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Continue reading
Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes. The ones who see things differently. They’re not fond of rules. And they have no respect for the status quo. You can quote them, disagree with them, glorify or vilify them. About the only thing you can’t do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.
Gavin E. Crooks, J. Stat. Mech. (2011) P07008
Abstract: The word ‘reversible’ has two (apparently) distinct applications in statistical thermodynamics. A thermodynamically reversible process indicates an experimental protocol for which the entropy change is zero, whereas the principle of microscopic reversibility asserts that the probability of any trajectory of a system through phase space equals that of the time reversed trajectory. However, these two terms are actually synonymous: a thermodynamically reversible process is microscopically reversible, and vice versa.
We all want progress, but if you’re on the wrong road, progress means doing an about-turn and walking back to the right road; in that case, the man who turns back soonest is the most progressive.
C. S. Lewis
I’ve been meaning to look at the physical significance of f-divergences for some time. These are a class of information type measures that, thanks to the quirks of nonequilibrium thermodynamics, can actually be experimentally measured in real systems. I was finally inspired to write this up due to John Baez, who recently discussed the significance of Rényi entropy to equilbrium statistical mechanics.
Abstract: Many interesting divergence measures between conjugate ensembles of nonequilibrium trajectories can be experimentally determined from the work distribution of the process. Herein, we review the statistical and physical significance of several of these measures, in particular the relative entropy (dissipation), Jeffreys divergence (hysteresis), Jensen–Shannon divergence (time-asymmetry), Chernoff divergence (work cumulant generating function), and Rényi divergence.
Super-duper-operator (n): An operator is a linear map that acts on a vector space. A superoperator is an operator of an operator, an operator that acts on a vector space of operators. A super-duper-operator is an operator of an operator of an operator, an operator that acts on a vector space of superoperators.