# Path function

In thermodynamics, path function is a one, two, or three dimensional Cartesian coordinate function whose magnitude depends on the path followed during a process as well as the end state. Path functions have inexact differentials. A path function, such as heat or work, are often contrasted with state functions, which are path independent and have exact differentials. [1] The difference between what constitutes a path function and a state function is bound up in the condition for an exact differential, which predates thermodynamics. In loose speak, according to American thermodynamicist Gordon van Wylen, the term 'point function' is synonymous with exact differential and the term 'path function' is synonymous with inexact differential. [1]

Related, albeit more complicated, conceptions include irreversible paths and reversible paths.

Few particle systems
There is some indication, according to computer simulations in nanothermodynamics (small system thermodynamics), that as system particle count becomes smaller, i.e. goes below about 1,000, and begins to decrease towards zero, path functions become state functions and state functions become path functions. [2]

Human thermodynamics

American thermodynamics professor Christopher Edwards, at Stanford University, teaches his students that, in thermodynamic terms, life is a path function: [3]

Life is a path function. You begin life, you end life—that's not so interesting, right? But quality of life is a path function. It's the path that you take from the beginning to the end, the integral of that path, that's the special part.”

Edwards explains that it is the choices one makes along the path that are the important steps.

References
1. Wylen, Gordon and Sonntag, Richard. (1973). Fundamentals of Classical Thermodynamics (pg. 71), 2nd ed. Wiley.
2. Mohazzabi, Pirooz, and Mansoori, G.A. (2005). “Nonextensivity and Nonintensivity in Nanosystems: A Molecular Dynamics Simulation.” Computational and Theoretical Nanoscience, 2: 1-10.
3. Levy, Dawn. (2006). “Professor of Thermodynamics Shares Best Practices for Teaching Tough Topics.” Stanford Report, Dec 05.

● Perrot, Pierre. (1998). A to Z of Thermodynamics (path function, pgs. 62, 106, etc.). Oxford University Press.
McQuarrie, Donald A. and Simon, John D. (1997). Physical Chemistry: a Molecular Approach (section 19-8: Heat capacity is a path function, pgs. 783-85). University Science Books.

What is the difference between a path function and a state function in thermodynamics? – WikiAnswers.
State function vs Path Function (2007) – PhysicsForums.com.
Why is heat a path function and not a state function? – YahooAnswers.