Dissipation

Dissipation is the result of irreversible processes that take place in inhomogeneous thermodynamic systems. A thermodynamic dissipative process is one in which energy, internal, bulk flow kinetic, or system potential, is transduced from some initial form to some final form, the capacity to do mechanical work of the final form being less that that of the initial form. For example, transfer of energy as heat is dissipative because it is a transfer of internal energy from a body at one temperature to a body at a lower temperature. The second law of thermodynamics implies that this reduces the capacity of that internal energy to do mechanical work.

Thermodynamic dissipative processes are essentially irreversible. They produce entropy at a finite rate. In a process in which the temperature is locally continuously defined, the local density of rate of entropy production times local temperature gives the local density of dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating). The concept of dissipation was introduced in the field of thermodynamics by William Thomson (Lord Kelvin) in 1852.

A particular occasion of occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energy—that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

Waves or oscillations, lose energy over time, typically from friction or turbulence. In many cases the "lost" energy raises the temperature of the system. For example, a wave that loses amplitude is said to dissipate. The precise nature of the effects depends on the nature of the wave: an atmospheric wave, for instance, may dissipate close to the surface due to friction with the land mass, and at higher levels due to radiative cooling.

In computational physics, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution.

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set.