Ehrenfest relation

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

Compressibility and pressure dependence of Curie temperature are directly measured changes in specific heat and thermal expansion are calculated from the Ehrenfest relation. 

There are two points to note about Eqs. (61) and (67). First, as they hold for any T, Eqs. (65) and (67) provide a general restatement of the Ehrenfest relations [34], that is, the quantum analog of the equations of motion of classical mechanics. Second, they embed a series of constraints among... 

Equations (186), (225), and (229) can be interpreted as relations involving generalized susceptibilities in a> space. In configuration space they are replaced by the Ehrenfest relations, written in terms of the observables (69)-(76). From (67) and... 

Nieuwenhuizen (2000) has shown that one of the Ehrenfest relations becomes... 

If the transition is second-order the Ehrenfest relation can be employed... 

For a second order phase transition like that of the normal superconducting state the pressure dependence of the transition temperature is related to the anomalies of the thermal expansion and the specific heat via the Ehrenfest relation ... 

An alternative is to make use of the thermodynamic Ehrenfest relation connecting the uniaxial stress (pt, i — x, y, or z) dependence of % with the discontinuity in the linear expansivity at Tp. 

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