Related papers: Non-Isothermal Electrokinetics: Energetic Variatio…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory can be formulated as an action principle…
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the…
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy…
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local…
For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept…
The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…
We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the…
The thermodynamic approach to non-equilibrium dynamics describes the state of macroscopic systems by means of a collection of intensities or intensive variables. The latter are by definition the differentials of the entropy with respect to…
Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…
While conventional hydrodynamics incorporating dissipative effects is hard to derive from an action principle, it is nevertheless possible to construct classical actions when the dissipative terms are switched off. In this note we undertake…
Equilibrium thermodynamics is grounded in the law of energy conservation, with a specific focus on how systems exchange energy with their environment during transitions between equilibrium states. These transitions are typically…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
We consider a theory of quantum thermodynamics with multiple conserved quantities (or charges). To this end, we generalize the seminal results of Sparaciari et al. [PRA 96:052112, 2017] to the case of multiple, in general non-commuting…
Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to…
Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics. This tutorial focuses on the derivation of the first and second law for closed and open quantum systems far from equilibrium, where…
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Nernst-Planck equations with variable temperature, and the…
A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…