sulting η/s at µ$_{B}$/T ≈ 0 . 13 is found to be similar to µ$_{B}$ = 0. In Fig. 4 we also illustrate the effect of high µ$_{B}$/T ≈ 3 . 0 associated with heavy ion collisions at the top AGS energy of √$_{s}$ = 4 . 85 GeV and at the lowest CERN/SPS energy of = 6 . 27 GeV [37, 38]; albeit the temperatures reached in these reactions are much smaller at T ∼ 125 − 145 MeV. We find that only for such large µ$_{B}$ the extracted η/s decreases further. The present study also suggests the need to incorporate, in the viscous hydrodynamics calculations, the Hagedorn states in the after-burning hadronic phase to quantify the dissipation and thus η/s ratio. While weakly coupled perturbative QCD estimate of η/s ≈ 1 at T ≫ T$_{c}$ , the QGP formed at RHIC in the re- gion T$_{c}$ ≤ T < ∼ 2 T$_{c}$ is thought to be strongly interacting. The current estimate of η/s ∼ 0 . 08 − 0 . 24 [6–8, 10, 39] at RHIC may be related to a minimum reached in the deconfined phase just above T$_{c}$ . Our estimate of η/s for the Hagedorn resonance gas suggests that, as the sQGP cools, the η/s in deconfined phase makes a relatively con- tinuous/smooth transition into the confined phase near T$_{c}$ without any discontinuity or a sharp increase proposed [24] in absence of Hagedorn states. In summary, we have studied the thermodynamic and transport properties of an infinite equilibrated matter composed of interacting hadron resonance gas plus an ex- ponentially increasing Hagedorn mass spectrum. At tem- peratures close to the Hagedorn temperature, T$_{H}$ = T$_{c}$ = 196 MeV, the particle densities of the massive resonances are enhanced significantly. This leads to a sharp rise in the trace anomaly and the entropy density of the sys- tem which captures the trend seen in the lattice data at vanishing baryon chemical potential. The shear viscosity to entropy density ratio of the Hagedorn resonance gas, both in and out of chemical equilibrium, decreases with temperature and baryon chemical potential and reaches a minimum of ( η/s )$_{min}$ ≈ 0 . 3 at about T$_{c}$ . The extracted minimum value is near the upper bound of current esti- mates for a strongly coupled quark-gluon plasma formed in ultra-relativistic heavy ion collisions at RHIC. I would like to thank Steffen Bass, Rajeev Bhalerao and Pawel Danielewicz for many helpful discussions. [7] P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99 [6] M.J. Tannenbaum, Rep. Prog. Phys. 69 (2006) 2005. [5] M. Gyulassy and L. McLerran, Nucl. Phys. A 750 (2005) 30; E.V. Shuryak, Nucl. Phys. A 750 (2005) 64. [4] K. Adcox et. al., Nucl. Phys. A 757 (2005) 184. [3] J. Adams et. al., Nucl. Phys. A 757 (2005) 102. [2] B.B. Back et. al., Nucl. Phys. A 757 (2005) 28. [1] I. Arsene et. al., Nucl. Phys. A 757 (2005) 1. [39] S. Pal, Phys. Rev. C 80 (2009) 041901(R). [38] G. Torrieri and J. Rafelski, Phys. Rev. C 75 (2007) 024902; J. Letessier and J. Rafelski, Eur. Phys. J. A 35 (2008) 221. [37] A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A 772 (2006) 167. [36] T. Hirano and M. Gyulassy, Nucl. Phys. A 769 (2006) 71. [35] K. Paech and S. Pratt, Phys. Rev. C 74 (2006) 014901. [34] A. Hosoya, M.-a. Sakagami, and M. Takao, Ann. Phys. (N.Y.) 154 (1984) 229. [33] R. Kubo, Rep. Prog. Phys. 29 (1966) 255. [32] S. Pal and S. Pratt, Phys. Lett. B 578 (2004) 310. [31] M. Belkacem et al., Phys. Rev. C 58 (1998) 1727. [30] J. Noronha-Hostler, J. Noronha and C. Greiner, Phys. Rev. Lett. 103 (2009) 172302. [29] B. Bringoltz and M. Teper, Phys. Rev. D 73 (2006) 014517; T.D. Cohen, Phys. Lett. B 637 (2006) 81. [28] T.D. Cohen, arXiv:0901.0492. [27] P. Castorina, J. Cleymans, D.E. Miller, and H. Satz, arXiv:0906.2289. [26] W. Broniowski and W. Florkowski, Phys. Lett. B 490 (2000) 223; W. Broniowski, W. Florkowski and L.Y. Glozman, Phys. Rev. D 70 (2004) 117503. [25] M. Cheng et al., Phys. Rev. D 77 (2008) 014511. [24] N. Demir and S.A. Bass, Phys. Rev. Lett. 102 (2009) 172302. [23] A. Muronga, Phys. Rev. C 69 (2004) 044901. [22] K. Itakura, O. Morimatsu and H. Otomo, Phys. Rev. D 77 (2008) 014014. [21] J.-W. Chen and E. Nakano, Phys. Lett. B 647 (2007) 371; J.-W. Chen, Y.-H. Li, Y.-F. Liu and E. Nakano, Phys. Rev. D 76 (2007) 114011. [20] A. Dobado and S.N. Santalla, Phys. Rev. D 65 (2002) 096011. [19] S. Pal, Phys. Rev. C 78 (2008) 011901(R). [18] S. Pal and P. Danielewicz, Phys. Lett. B 627 (2005) 55. [17] R. Venugopalan and M. Prakash, Nucl. Phys. A 546 (1992) 718. [16] J.I. Kapusta and K.A. Olive, Nucl. Phys. A 408 (1983) 478. [15] R. Hagedorn and J. Rafelski, Phys. Lett. B 97 (1980) 136. [14] J.-P. Blaizot, J. Phys. G 34 (2007) S243. [13] R. Lacey et al., Phys. Rev. Lett. 98 (2007) 092301. [12] L.P. Csernai, J.I. Kapusta and L.D. McLerran, Phys. Rev. Lett. 97 (2006) 152303. [11] P. Arnold, G.D. Moore and L.G. Yaffe, JHEP 05 (2003) 051. [10] H.B. Meyer, Phys. Rev. D 76 (2007) 101701. [9] G. Policastro, D.T. Son, and A.O. Starinets, Phys. Rev. Lett. 87 (2001) 081601; P.K. Kovtun, D.T. Son and A.O. Starinets Phys. Rev. Lett. 94 (2005) 111601. [8] H. Song and U. Heinz, Phys. Lett. B 658 (2008) 279. (2007) 172301; M. Luzum and P. Romatschke, Phys. Rev. C 78 (2008) 034915. 5