Related papers: Path-Dependent Energy Lagrangian for Irreversible …
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…
A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…
The variational approach usually used in phase field models (PFVA) is applied here to analyse complex irreversible processes such as thermoelectric (TE) effects and thermally driven mass transport (TDMT). Complex irreversible processes…
We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat…
We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and…
We consider a Brownian particle confined by an external potential and subject to stochastic resetting to the origin. Motivated by the repetitive nature of the dynamics, we describe the process as a thermodynamic cycle of thermal expansion…
Extended irreversible thermodynamics is a theory that expands the classical framework of nonequilibrium thermodynamics by going beyond the local-equilibrium assumption. A notable example of this is the Maxwell-Cattaneo heat flux model,…
In this paper we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
When the process of a system in contact with a heat bath is described by classical Langevin equation, the method of stochastic energetics [K. Sekimoto, J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of Helmholtz free…
The present work deals with irreversible Universal thermodynamics. The homogenous and isotropic flat model of the universe is chosen as open thermodynamical system and non-equilibrium thermodynamics comes into picture due to the mechanism…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
Despite its simplicity, it seems to my best of knowledge that the possibly simplest approach towards deriving equations governing irreversible thermodynamics from gas-kinetic considerations within the framework of classical mechanics has…
We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
In addition to the Riemannian metricization of the thermodynamic state space, local relaxation times offer a natural time scale, too. Generalizing existing proposals, we relate {\it thermodynamic} time scale to the standard kinetic…
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative…
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…