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- The rates of approach to equilibrium in real materials are found experimentally to depend on gradients of thermodynamic potentials
In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.
In thermodynamics, thermodynamic potentials are parameters associated with a thermodynamic system and have the dimensions of energy. They are called "potentials" because in a sense, they describe the amount of potential energy in a thermodynamic system when it is subjected to certain constraints. The different potentials correspond to different constraints to which the system may be subjected.
- * A scalar field associates a physical quantity with position--e.g. a composition field
In mathematics and physics, a scalar field associates a scalar value, which can be either mathematical in definition, or physical, to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. In mathematics, or more specifically, differential geometry, the set of functions defined on a manifold define the commutative ring of functions. A gradient of a scalar field is a vector that quantifies how rapidly the field changes with position
- The flux of a substance quantifies the rate at which that substance flows through a unit area. The flux is a vector that is parallel to the local direction of the flow.
- The rate of accumulation of an extensive quantity is minus the divergence of the flux of that quantity plus the rate of production of the substance.
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