Ehrenfest scheme for complex thermodynamic systems in full phase space

TL;DR

This paper extends Ehrenfest equations to complex thermodynamic systems with multiple variables, providing a method to determine phase boundary dimensions and applying it to RN-AdS black holes.

Contribution

It introduces two classes of Ehrenfest equations in full phase space for systems with multiple variables, linking matrix rank to phase boundary dimensions.

Findings

Derived Ehrenfest equations for multi-variable systems.

Linked matrix rank to phase boundary dimension.

Applied framework to RN-AdS black hole.

Abstract

For a thermodynamic system with multiple pairs of intensive/extensive variables and the thermodynamical coefficients attain finite or infinite values on the phase boundary, we obtain the two classes of Ehrenfest equations in the full phase space, and find that the rank of the matrix for these equations can tell us the dimensions of the phase boundary. We also apply this treatment to the RN-AdS black hole.