Diffusion is the phenomenon of random motion causing a system to decay towards uniform conditions. For example, diffusion of particles causes a net movement of particles from areas of higher concentration to areas of lower concentration until equilibrium is reached. This is simply the statistical outcome of random motion: diffusion is a spontaneous process (more familiarly known as a "passive" form of transport, rather than "active"). Diffusion can affect a variety of different quantities. Examples include diffusion of concentration, heat, or momentum. Diffusion increases entropy, decreasing Gibbs free energy, and therefore is thermodynamically favorable.
Net movement is an important topic in physical and engineering science. It involves the overall migration of particles, molecules or other constituent particles within a system from one portion of the system to another.
The different forms of diffusion can be modeled quantitatively using the diffusion equation, which goes by different names depending on the physical situation. For instance - steady-state bi-molecular diffusion is governed by Fick's law, steady-state thermal diffusion is governed by Fourier's law. The diffusion of electrons in an electrical field leads essentially to Ohm's law that is further explained by Einstein relation. The generic diffusion equation is time dependent, and as such applies to non-steady-state situations as well.
In all cases of diffusion, the flux of the transported quantity (atoms, energy, or electrons) is equal to a physical property (diffusivity, thermal conductivity, electrical conductivity) multiplied by a gradient (a concentration, thermal, electric field gradient). Noticeable transport occurs only if there is a gradient - for example in thermal diffusion, if the temperature is constant, heat will move as quickly in one direction as in the other, producing no net heat transport or change in temperature.
The second law of thermodynamics states that in a spontaneous process, the entropy of the universe increases. Change in entropy of the universe is equal to the sum of the change in entropy of a system and the change in entropy of the surroundings. A system refers to the part of the universe being studied; the surroundings is everything else in the universe. Spontaneous change results in dispersal of energy. Spontaneous processes are not reversible and only occur in one direction. No work is required for diffusion in a closed system. Reversibility is associated with equilibrium. Work can be done on the system to change equilibrium. Energy from the surroundings decrease by the amount of work expended from surroundings. Ultimately, there will be a greater increase in entropy in the surroundings than the decrease of entropy in the system working accordingly with the second law of thermodynamics.
Diffusion can be measured, by the means of concentration gradient. A concentration gradient is the difference between the high concentration and the low concentration. It also determines how fast diffusion occurs.
Diffusion in a continuum may be quantified through the Laplacian. This is widely seen in heat transfer (diffusion of heat), chemistry (diffusion of chemical species), fluid mechanics (diffusion of momentum), thermodynamics (diffusion of energy quality) and elsewhere.