A great step forward towards the understanding of high temperature
superconductors are the variety of experimental results which have led to the
wide-spread acceptance of the idea that a phase with a broken symmetry competes
with superconductivity in the under-doped region, often called the pseudo-gap
region. There are a plethora of suggested phases. The idea, that a broken
symmetry phase competes with superconductivity makes thermodynamic sense only
if the energy gained due to it is comparable to that gained through the
superconducting transition in their co-existence region. Extraordinarily,
however, no specific heat signature of a phase transition has been identified
at the pseudo-gap temperature T∗. We use the recent highly accurate
sound-velocity measurements and the best available specific heat measurements
in YBa2Cu3O6+δ to show that phase transitions to the
universality class of the loop-current ordered state with free-energy reduction
similar to the measured superconducting condensation are consistent with the
sound velocity and with lack of identifiable observation in the specific heat.
We also compare the measured specific heat with some more usual transitions and
show that transitions with such symmetry classes can easily be shown by
existing specific heat measurements to have energy reduction due to them less
than 1/20 the superconducting condensation energy