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History

The so-called Pfaffian form, supposedly, was derived in circa 1805 by German mathematician Johann Pfaff.

Truncated Pfaffian

The expression:

where W is an amount of work done by the system, Y is an intensive property of the system, and Z is an extensive property of the system, is called a "truncated Pfaffian". [3]

Note

The Pfaffian expression is somehow related to the so-called Maxwell relations as found in the thermodynamic work of James Maxwell. [3]

Etymology

The names Pfaffian form, Pfaffian function, Pfaffian expression, truncated Pfaffian, etc., may have been introduced in Greek mathematician Constantin Caratheodory's 1908 "Studies in the Foundation of Thermodynamics", and what has since been called Caratheodory's theorem; although this needs to be fact-checked.

Another reference seems to state that the names Pfaffian function and Pfaffian form for these types of expressions were introduced in the 1970s by Russian mathematician

Conjugate variables

Pfaffian forms is a common formulation in thermodynamics, where the summation pairs, each taking the form of intensive (Xi) and extensive (xi) conjugate variable pair, act as quantifiable energy representations of transformations of the internal energy of the system. The right side of the Gibbs fundamental equation, for example, is a Pfaffian form. In short, the general use of the conjugate pairs perspective is that one can quantify the internal energy of a system as the sum of the conjugate variables. In short, with any extensitySee main: Conjugate variables

which is called the "conjugate", whereby, according to the first law, the change in internal energy

The combined law of thermodynamics:

being the simplest example, temperature

References

1. Sychev, Viacheslav V. (1991).

2. Caratheodory, Constantin. (1908).

3. Kestin, Joseph. (1966).

Further reading

● Sychev, Viacheslav. (1981).

● Emanuel, George. (1987).

● Ott, Bevan J. and Boerio-Goates Juliana. (2000).

External links

● Pfaffian function – Wikipedia.

● Pfaffian form – Wolfram MathWorld.