Volume 40, Issue 2

We propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing numerics. More importantly, CDF is a genuinely nonlinear formalism and works for systems far away from equilibrium. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows as two typical examples. In these examples, the non-equilibrium variables are exactly the conjugate variables of the heat fluxes or stress tensors. The new theory generalizes Cattaneo's law or Maxwell's law in a regularized and nonlinear fashion.

We study contact stress relaxation timescales, especially the temporal correlation involved in dense binary particulate systems, which offers insight into the intriguing relationship between the contact stresses and the contact time of particle interactions under non-equilibrium state. The contact time (also referred to as contact age) of a pair of particles is defined by the duration between current time and the instant when the contact was formed. The interspecies inter-particles contact stresses are derived from Liouville's theorem. We apply particle dynamics methods (e.g. molecular dynamics, discrete element method) to simulate 3D dense binary particulate systems with periodic boundary conditions. External perturbation is exerted on the system to balance the dissipation of energy due to the viscoelastic collisions. The contact stresses, Reynolds stresses, and the probability density function of the contact time of particles are predicted at different volume fraction of particles. The obtained stress-strain rate data are used to examine the constitutive relation of macroscopic materials. The study targets the impact of the short-term and the long-term contact/collision on the contact stress relaxation. The simulation results reveal distinct effects of the short-term and the long-term contact/collision on the contact stresses, which have been treated by only an averaged expression of particle interactions in discrete element methods before.

Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field [J. Non-Equilib. Thermodyn. 38 (2013), 141–151]. The treatment in that work was limited to a four-dimensional Minkowski space-time in which the Boltzmann equation was treated in a special relativistic approach. The more complete framework of general relativity can be introduced to kinetic theory in order to describe transport processes associated to electromagnetic fields. In this context, the original Kaluza's formalism is a promising approach [Sitz. Ber. Preuss. Akad. Wiss. (1921), 966–972; Gen. Rel. Grav. 39 (2007), 1287–1296; Phys. Plasmas 7 (2000), 4823–4830]. The present work contains a kinetic theory basis for Kaluza's magnetohydrodynamics and gives a novel description for the establishment of thermodynamic forces beyond the special relativistic description.

Laser short-pule irradiation of silicon-diamond-aluminum thin films is considered and energy transport across the films is modelled using the Boltzmann transport equation. Electron-phonon coupling is adopted to formulate energy transfer across the electron and lattice sub-systems in the aluminum film. Thermal boundary resistance is incorporated at the film interfaces. The transfer matrix method is used to account for the transmittance, reflection and absorption of the incident laser radiation across the films. Equivalent equilibrium temperature is introduced to access energy transport in the films, which represents the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. It is found that equivalent equilibrium temperature increases sharply in the electron sub-system due to electron excess energy gain from the irradiated field. Equivalent equilibrium temperature decays gradually in the lattice sub-system with increasing period due to phonon scattering in the film.

The availability of a thermodynamic system out of equilibrium with its environment describes its ability to perform work in a reversible process which brings it to equilibrium with this environment. Processes in finite time can usually not be performed reversibly thus leading to unavoidable losses. In order to account for these losses the concept of finite time availability was introduced. We here add a new feature through the introduction of quantum finite time availability for an ensemble of parametric oscillators. For such systems there exists a certain critical time, the FEAT time. Quantum finite time availability quantifies the available work from processes which are shorter than the FEAT time of the oscillator ensemble.