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Examples of path functions include work, heat and arc length. In contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function.
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...
When a system undergoes a change from one state to another, it is said to traverse a path. The path can be described by how the properties change, like isothermal (constant temperature) or isobaric (constant pressure) paths. Thermodynamics sets up an idealized conceptual structure that can be summarized by a formal scheme of definitions and ...
An inexact differential is a differential for which the integral over some two paths with the same end points is different. Specifically, there exist integrable paths ,: [,] such that () = (), () = and In this case, we denote the integrals as | and | respectively to make explicit the path dependence of the change of the quantity we are considering as .
A curve in a topological space is a continuous function: from a non-empty and non-degenerate interval. A path in is a curve : [,] whose domain [,] is a compact non-degenerate interval (meaning < are real numbers), where () is called the initial point of the path and () is called its terminal point.
A path from a point x to a point y in a topological space X is a continuous function f from the unit interval [0,1] to X with f(0) = x and f(1) = y. A path-component of X is an equivalence class of X under the equivalence relation, which makes x equivalent to y if there is a path from x to y. The space X is said to be path-connected (or ...
A scalar function whose contour lines define the streamlines is known as the stream function. Dye line may refer either to a streakline: dye released gradually from a fixed location during time; or it may refer to a timeline: a line of dye applied instantaneously at a certain moment in time, and observed at a later instant.
Suppose that = for some (continuously differentiable) scalar field [3] over as an open subset of (so is a conservative vector field that is continuous) and is a differentiable path (i.e., it can be parameterized by a differentiable function) in with an initial point and a terminal point .