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Irreversible entropy production (IEP) plays an important role in quantumthermodynamic processes. Here we investigate the geometrical bounds of IEP innonequilibrium thermodynamics by exemplifying a system coupled to a squeezedthermal bath subject to dissipation and dephasing, respectively. We find thatthe geometrical bounds of the IEP always shift in contrary way underdissipation and dephasing, where the lower and upper bounds turning to betighter occurs in the situation of dephasing and dissipation, respectively.However, either under dissipation or under dephasing, we may reduce both thecritical time of the IEP itself and the critical time of the bounds forreaching an equilibrium by harvesting the benefits of squeezing effects, inwhich the values of the IEP, quantifying the degree of thermodynamicirreversibility, also becomes smaller. Therefore, due to the nonequilibriumnature of the squeezed thermal bath, the system-bath interaction energy bringsprominent impact on the IEP, leading to tightness of its bounds. Our resultsare not contradictory with the second law of thermodynamics by involvingsqueezing of the bath as an available resource, which can improve theperformance of quantum thermodynamic devices.

Geometrical bounds on irreversibility in squeezed thermal bath