Third order viscous hydrodynamics from the entropy four current

Non-equilibrium dynamics for relativistic fluid or quark gluon plasma (QGP) have already been calculated earlier upto third order using both kinetic and thermodynamic approaches. Calculations presented in this manuscript are based on thermodynamics principles. The expressions for third order dissipative fluxes have been derived from equation for entropy 4-current developed earlier by A. Muronga. The relaxation equations in the present work have been developed in a simple Bjorken (1+1)D scenario and Eckart frame. The relaxation equations are found to have slightly different values for the coupling coefficients as compared to calculations from earlier models. The solutions to the differential equations have been found to be sensitive to values of these coefficients. The shear relaxation equations derived in third order theory are discussed term by term. Effects of third order theory on shear relaxation time has been discussed. Thermodynamic quantities related to hot and dense matter have been calculated as functions of proper time. Moreover, various initial conditions for the relaxation equations have been assumed to study their effects on above mentioned observables. A LHC QGP formation time of $\tau_0$ = 0.4 fm/c and temperature of T$_0$ = 500 MeV have been assumed.