Related papers: A microscopic view on the Fourier law
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…
We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and…
We describe a simple framework for teaching the principles that underlie the dynamical laws of transport: Fick's law of diffusion, Fourier's law of heat flow, the Newtonian viscosity law, and mass-action laws of chemical kinetics. In…
A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally…
This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
Size-dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and…
Heat flow and thermal profile in a 1D harmonic lattice with coordinate-dependent masses has been calculated in the thermodynamic limit. It is shown in the particular example of a 1D harmonic lattice with linearly increasing masses that in…
Thermal conductivities are routinely calculated in molecular dynamics simulations by keeping the boundaries at different temperatures and measuring the slope of the temperature profile in the bulk of the material, explicitly using Fourier's…
The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment…
A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the…
We establish a connection between anomalous heat conduction and anomalous diffusion in one dimensional systems. It is shown that if the mean square of the displacement of the particle is $<\Delta x^2> =2Dt^{\alpha} (0<\alpha\le 2)$, then…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…
Understanding thermal transport from nanoscale heat sources is important for a fundamental description of energy flow in materials, as well as for many technological applications including thermal management in nanoelectronics,…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
In a thermodynamical process, the dissipation or production of entropy can only be positive or zero according to the second law of thermodynamics. However the laws of thermodynamics are applicable to large systems in the thermodynamic…