This paper att empts to give a unified approach to the existing three types of variational principles for vector valued functions: A. B. Nemeth (1986), Chr. Tammer (1992) and G. Isac (1996). Some of the results we obtain are variants of the authors' mentioned above. Some are even stronger than...

A variational principle for heat conduction is formulated which results in the steady state heat conduction equation established from the Fourier law. Furthermore based on the thermodynamics in terms of entransy a more general functional is defined for incompressible fluids. We show that...

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...

We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax–Oleĭnik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a...