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The equation of state of the triclinic compound 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) as well as its second-order isothermal elastic tensor were computed through classical molecular dynamics simulations under various temperature and pressure conditions. Hydrostatic pressures similar to previous diamond anvil cell experiments were imposed within the range [0, 66] GPa and temperatures chosen between 100 and 900 K in conjunction with the most recent version of an all-atom fully-flexible molecule force field. The isothermal elastic constants were computed using the generalized Hooke's law by fitting Cauchy stress vs. linear strain curves. Along isobaric pathways, TATB single crystal stiffness is found to undergo linear softening, less pronounced at high pressure, while maintaining its elastic anisotropy. On the other hand, along an isothermal pathways, a non-linear increase is observed in the elastic constants with a significant decrease in anisotropy. Towards a precise mesoscopic modeling of TATB single crystal mechanical behavior, we provide "ready to plug-in" analytical formulations of the P,V,T equation of state and pressure-temperature dependent non-linear elasticity.