There are growing experimental evidence which indicate discrete symmetry breaking like parity, time-reversal and C4 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 pseudogap temperature T * . In this work, we investigate thermodynamic signature of parity and time-reversal symmetry breaking within a theory of two kinds of instabilities in particle-particle (p-p) and particle-hole (p-h) channels in the pseudo-gap state. The p-p and p-h instabilities correspond to superconductivity (SC) and bond-excitonic (BDW) orders respectively. The BDW can generate both modulating charge and current densities. This scenario leads to an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the under-doped regime. We show that a mean-field ground state of coexisting BDW and SC can spontaneously break the parity and time-reversal symmetry below superconducting critical temperature, provided the BDW itself breaks the time-reversal and parity. We describe that an auxiliary order parameter, referred as magneto-electric loop current (MELC) order, can be constructed from a composite of BDW and SC fields. We demonstrate that the MELC order spontaneously breaks parity and time-reversal symmetry and emerges due to a preemptive phase transition at a higher temperature before the primary orders set in.