system with a high thermal resistance (comparatively low conductivity) plays the role of the resistor in the circuit. Relativistic conduction The theory of relativistic heat conduction is a model that is compatible with the theory of special relativity. For most of the last century, it was recognized that the Fourier equation is in contradiction with the theory of relativity because it admits an infinite speed of propagation of heat signals. For example, according to the Fourier equation, a pulse of heat at the origin would be felt at infinity instantaneously. The speed of information propagation is faster than the speed of light in vacuum, which is physically inadmissible within the framework of relativity. Quantum conduction Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to a very high thermal conductivity. It is known as "second sound" because the wave motion of heat is similar to the propagation of sound in air. Fourier's law The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally. Newton's law of cooling is a discrete analogue of Fourier's law, while Ohm's law is the electrical analogue of Fourier's law and Fick's laws of diffusion is its chemical analogue. Differential form The differential form of Fourier's law of thermal conduction shows that the local heat flux density is equal to the product of thermal conductivity and the negative local temperature gradient . The heat flux density is the amount of energy that flows through a unit area per unit time. where (including the SI units) is the local heat flux density, W/m2, is the material's conductivity, W/(m·K), is the temperature gradient, K/m. The thermal conductivity is often treated as a constant, though this is not always true. While the thermal conductivity of a material generally varies with