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Recent studies indicate that, near equilibrium condition could not bemaintained for bulk viscous matter models during the accelerated expansion ofthe universe in the context of Einstein's gravity, without including thecosmological constant. But from our investigation in $f(R,T)$ gravity, it isobserved that, this condition can be satisfied in this modified gravity regimeby properly constraining the coupling and viscous parameters. Accordingly,strict constraints are developed for free parameters in bulk viscous models in$f(R,T)=R+2\lambda T$ gravity based on fulfillment near equilibrium condition.Then, for assessing the validity of NEC during different stages of evolution,two cosmological models are studied for each case based on the developedconstraints. Initially, the data analysis of the models is performed using theObservational Hubble Data (OHD) and then later, model showing the best resultis analyzed using combined OHD+SNe Ia data sets. From the obtained best fitvalues of model parameters, inferences are made regarding the possibilities ofachieving recent acceleration for viscous models in $R+2\lambda T$ gravitywhile simultaneously satisfying the required conditions both in the presenceand absence of cosmological constant.

Near Equilibrium Constraints on Bulk Viscous Models in $f(R,T)=R+2\lambda T$ Gravity