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Since its experimental discovery, many phenomenological theories successfullyreproduced the rapid rise from $p$ to $1+p$ found in the Hall number $n_H$ atthe critical doping $p^*$ of the pseudogap in superconducting cuprates. Furthercomparison with experiments is now needed in order to narrow down candidates.In this paper, we consider three previously successful phenomenologicaltheories in a unified formalism---an antiferromagnetic mean field (AF), aspiral incommensurate antiferromagnetic mean field (sAF), and theYang-Rice-Zhang (YRZ) theory. We find a rapid rise in the specific heat and arapid drop in the Seebeck coefficient for increasing doping across thetransition in each of those models. The predicted rises and drops are locked,not to~$p^*$, but to the doping where anti-nodal electron pockets,characteristic of each model, appear at the Fermi surface shortly before~$p^*$.While such electron pockets are still to be found in experiments, we discusshow they could provide distinctive signatures for each model. We also show thatthe range of doping where those electron pockets would be found is stronglyaffected by the position of the van~Hove singularity.

Phenomenological theories of the low-temperature pseudogap: Hall number, specific heat and Seebeck coefficient