Related Experiment Video
Updated: Aug 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Loop calculus in statistical physics and information science
Michael Chertkov1, Vladimir Y Chernyak
1Theoretical Division and Center for Nonlinear Studies, LANL, Los Alamos, New Mexico 87545, USA.
Abstract:
Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (belief propagation) (BP) contribution; the rest are expressed as loop contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed.
Related Concept Videos
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs
On the other hand, integral calculus focuses on...
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Statements of the Second Law of Thermodynamics
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

