- The local entropy production in a system can expressed as a sum of terms, each of which is a product of a flux and a conjugate "force"
In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time, the volumetric flow rate. Flux in this definition is a vector.
In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as pressure/volume or temperature/entropy. In fact all thermodynamic potentials are expressed in terms of conjugate pairs.
For a mechanical system, a small increment of energy is the product of a force times a small displacement. A very similar situation exists in thermodynamics. An increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" which, when imbalanced cause certain generalized "displacements", and the product of the two is the energy transferred as a result. These forces and their associated displacements are called conjugate variables. The thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yielding an extensive energy transfer. The intensive (force) variable is the derivative of the internal energy with respect to the extensive (displacement) variable, while all other extensive variables are held constant.
- Familiar empirical laws are linear relationships between fluxes and their conjugate forces: Fourier's law of heat conduction, Fick's law for diffusion, and Ohm's law for electrical conduction (see KoM Table 2.1)
A scientific law, or empirical law, is a general principle that is very well supported by evidence such as experimental results and observational data. Typically scientific laws are limited sets of rules that have a well documented history for successfully predicting the outcomes of experiments and observations.
The law of heat conduction, also known as Fourier's law, states that the rate, in time, 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 in flowing
Fick's first law is used in steady-state diffusion, i.e., when the concentration within the diffusion volume does not change with respect to time
Ohm's law states that, in an electrical circuit, the current passing through a conductor, from one terminal point on the conductor to another terminal point on the conductor, is directly proportional to the potential difference (i.e. voltage drop or voltage) across the two terminal points and inversely proportional to the resistance of the conductor between the two terminal points.
- The basic postulate of irreversible thermodynamics is that, near equilibrium, the local entropy production is non-negative (see KoM Eq 2.16). This postulate dictates that material properties such as thermal conductivity in heat flow and atomic mobility in diffusion are inherently positive quantities.
Irreversible thermodynamics attempts to apply thermodynamics principles to systems that are not in equilibrium and to suggest principles by which they relax toward equilibrium or steady state.
In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat.
- When more than one force is active, each force will generally cause a flux of its corresponding quantity; such pairings are called direct couplings between forces and their conjugate fluxes. There also may be cross terms that relate a flux to the magnitudes of its non-conjugate forces.
- When several forces are active and a system is "near" equilibrium, the flux of a given quantity is postulated to be linearly related to all of the forces (see KoM Eqs 2.20 - 21)
- The potential which appears is the total conjugate force acting on a diffusing component i in a material is called the diffusion potential. The driving force for the diffusing component is given by the negative gradient of the diffusion potential.
In physics, a potential may refer to the scalar potential or to the vector potential. In either case, it is a field defined in space, from which many important physical properties may be derived. Leading examples are the gravitational potential and the electric potential, from which the motion of gravitating or electrically charged bodies may be obtained.
A terminology used in thermodynamics expressing the availability of energy to 'drive' a process such as mechanical work or chemical synthesis. Driving forces exist where a potential gradient exist. A potential gradient can be in form of a temperature gradient causing heat to flow, an electrical gradient causing electrons or ions to flow, or a concentration gradient causing diffusion.
- According to Onsager's symmetry principle, the matrix of coupling coefficients in the system of linear equations is postulated to be symmetric.