Related papers: Balance Systems and the Variational Bicomplex
This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…
We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we deduce the equation of motions, the action…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics
The Lindbladian formalism models open quantum systems using a 'bottom-up' approach, deriving linear dynamics from system-environment interactions. We present a 'top-down' approach starting with phenomenological constraints, focusing on…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…
In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions…
In this work, bi-para-complex analogue of Lagrangian and Hamiltonian systems was introduced on Lagrangian distributions. Yet, the geometric and physical results related to bi-para-dynamical systems were also presented.
Optical, acoustic, hydrodynamic, and thermal defect systems are often studied by analogy with each other. This may indicate that we may find a emergent theory for constitutive relations of classical defect systems. Start with thermal…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
This paper is devoted to hyperbolic systems of balance laws with non local source terms. The existence, uniqueness and Lipschitz dependence proved here comprise previous results in the literature and can be applied to physical models, such…
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…