  There are growing experimental evidence which indicate discrete symmetry
breaking like time-reversal ($\mathcal{T}$), parity ($\mathcal{P}$) and C$_{4}$
lattice rotation in the pseudo-gap state of the under-doped copper-oxide based
(cuprate) superconductors. The discrete symmetry breaking manifests a true
phase transition to an ordered state. A detailed thermodynamic understanding of
these orders can answer various puzzles related to the nature of the transition
at the pseudo-gap temperature T$^*$. In this work, we investigate thermodynamic
signature of $\mathcal{T-P}$ symmetry breaking considering superconductivity
(SC) and bond-density wave (BDW) as two primary orders. The BDW can generate
both modulating charge and current densities. This framework takes into account
an intricate competition between the ubiquitous charge density wave and SC,
which is prominent in various cuprates in the under-doped regime. We
demonstrate that within mean-field approach of competing BDW and SC orders, a
$\mathcal{T-P}$ breaking ground state of coexisting BDW and SC can be
stabilized, provided the BDW itself breaks $\mathcal{T}-\mathcal{P}$. But this
ground state ceases to occur at higher temperatures. However, we show that
fluctuations in SC and BDW can drive emergence of a new unusual translational
symmetry preserving order due to a preemptive phase transition by spontaneously
breaking $\mathcal{T-P}$ at a higher temperature before the primary orders set
in. We refer this order to be magneto-electric loop current (MELC) order. We
present possible nature of phase transition for this new incipient MELC order
and discuss some experimental relevance.
