In recent years, there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis. Most of these kinds of contributions are suggested by some quantum statistical physics problems or...

We present a global variational definition of a vortex core in three-dimensional flows, and describe its implementation for tracking principal vortex cores in a viscous fluid. Our definition is motivated by the observation that the line integral of vorticity along any path worthy of being called...

Using information theory, a new variational principle for incompressible fluids is derived. This principle is similar to a known plasma stability criterion which has successfully been applied to study the stability of different steady flows. Its main advantages, when compared to traditional...

The mechanism of entropy production in transport phenomena is discussed again by emphasizing the role of symmetry of non-equilibrium states and also by reformulating Einstein’s theory of Brownian motion to derive entropy production from it. This yields conceptual reviews of the previous papers...

A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum...