Several identities in statistical mechanics

Several Constants Arising in Statistical Mechanics

Random lattice models give rise to combinatorial problems that are often easily-stated but intractable. This article briefly presents several such problems, each involving the numerical estimation of asymptotic growth constants. Emphasis is given to recent developments. The author has been collecting and writing about various mathematical constants for five years. His large evolving website [18...

Several Series Identities Involving the Catalan Numbers

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Justification in Statistical Mechanics

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fun...

Statistical Mechanics

Interventionism in Statistical Mechanics

I defend the idea that the fact that no system is entirely isolated (“Interventionism”) can be used to explain the successful use of the microcanonical distribution in statistical mechanics. The argument turns on claims about what is needed for an adequate explanation of this fact: I argue in particular that various competing explanations do not meet reasonable conditions of adequacy, and that ...