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The fluctuation–dissipation theorem is a general result of statistical thermodynamics that quantifies the relation between the fluctuations in a system that obeys detailed balance and the response of the system to applied perturbations.
Atomic diffusion on the surface of a crystal. The shaking of the atoms is an example of thermal fluctuations. Likewise, thermal fluctuations provide the energy necessary for the atoms to occasionally hop from one site to a neighboring one. For simplicity, the thermal fluctuations of the blue atoms are not shown.
These exact results are particularly relevant for small systems where appreciable (typically non-Gaussian) fluctuations occur. Thanks to stochastic thermodynamics it is now possible to accurately predict distribution functions of thermodynamic quantities relating to exchanged heat, applied work or entropy production for these systems.
This random motion is described by a differential equation, known as the diffusion equation. The diffuson is the Green's function of the diffusion equation. [1] The diffuson plays an important role in the theory of electron transport in disordered systems, especially for phase coherent effects such as universal conductance fluctuations. [3]
D is the diffusion coefficient; μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = v d /F; k B is the Boltzmann constant; T is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. [7]
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
3D visualization of quantum fluctuations of the quantum chromodynamics (QCD) vacuum [1]. In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, [2] as prescribed by Werner Heisenberg's uncertainty principle.
In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale. [3] Chemical diffusion increases the entropy of a system, i.e. diffusion is a spontaneous and irreversible process. Particles can spread out by diffusion, but will not spontaneously re-order themselves ...