Related papers: A Model of Heat Conduction
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its fluctuations. Based on a generalized Onsager-Machlup theory…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
The constant temperature derivation, which is a model-free derivation of the Boltzmann factor, is generalized in order to develop a new simple model-free derivation of a power-law Tsallis factor based on an environment with constant heat…
We propose a new one-dimensional lattice model with strong asymmetric interaction potential and investigate heat conduction in this model numerically. We find that Fourier law is obeyed. Based on the phonon theory, we find a new scattering…
In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a…
A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…
We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this…
We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
We consider a simple one dimensional stochastic model of heat transport which locally conserves both energy and momentum and which is coupled to heat reservoirs with different temperatures at its two ends. The steady state is analyzed and…
Heat transport exhibits distinct regimes ranging from ballistic propagation to diffusive relaxation, traditionally described by disparate theoretical frameworks. Here, we introduce a unified first-order operator formulation in which…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in…
The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities…
Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that…
We present a microscopic Hamiltonian framework to develop Maxwell demon like engine. Our model consists of a equilibrium thermal bath and a non-equilibrium bath; latter generated by driving with an external stationary, Gaussian noise. The…
We consider a one-dimensional partial differential equation system modeling heat flow around a ring. The system includes a Klein-Gordon wave equation for a field satisfying spatial periodic boundary conditions, as well as Ornstein-Uhlenbeck…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…