## Thermodynamic identities

Posted by peeterjoot on March 7, 2013

Impressed with the clarity of Baez’s entropic force discussion on differential forms [1], let’s use that methodology to find all the possible identities that we can get from the thermodynamic identity (for now assuming is fixed, ignoring the chemical potential.)

This isn’t actually that much work to do, since a bit of editor regular expression magic can do most of the work.

Our starting point is the thermodynamic identity

or

It’s quite likely that many of the identities that can be obtained will be useful, but this should at least provide a handy reference of possible conversions.

**Differentials in **

This first case illustrates the method.

Taking wedge products with and respectively, we form two two forms

Since these must both be zero we find

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

**Differentials in **

or

# References

[1] John Baez. *Entropic forces*, 2012. URL http://johncarlosbaez.wordpress.com/2012/02/01/entropic-forces/. [Online; accessed 07-March-2013].

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