4 different time. Our current approach does not take such a space-time picture but just provide an averaged ef- fect which is more simple and transparent than a real hydrodynamic simulation. If combination is treated lo- cally one can still compute the entropies before and after hadronization for each space-time cell using Eq. (2) or Eqs. (5-6). The total entropy is a sum over all cells and the result is similar to the ideal case in our paper. This implies that the entropy can be described in a global and effective way as in our current model. In other words the entropy is a global quantity which should be insensi- tive to the local fine structure. As we have emphasized in the beginning that we do not address in our QCM the entropy issue in the context of phase transition. We just made a few comments about it. If local equilirium is reached for a closed system the entropy would not change during the transition from the quark to hadronic phase, it is the entropy density that changes (decreases) during the transition acompanied by the volume expansion. If the system is not in local equilibrium the phase transi- tion is not well defined (it is indeed a crossover) but still one can obtain the total entropy which should increase. Such a study in the QCM is independent of whether the entropy increases or decreases beyond the combination process. In summary, we have investigated the issue of the en- tropy in the framework of the quark combination-like model. As an example for such types of models we used the one developed by Shandong group whose exclusive nature makes a transparent calculation feasible. We used two available methods to calculate the entropies for the quark and hadronic phases, one from the Duhem-Gibbs relation, another from the entropy formula in terms of particle phase space distributions. We found that the total entropy from the Duhem-Gibbs relation always in- creases in hadronization if the average temperature of the hadronic phase is lower than that of the quark phase. The increase of the entropy during hadronization can also be confirmed from the entropy formula if the volume of the hadronic phase is larger than 2.5-3.0 times that of the quark phase. This implies that the expansion of the fireball takes place during hadronization and it takes fi- nite time for the quark phase to hadronize. So whether the entropy increases or decreases during combination de- pends on the temperature before and after combination and on how much expansion the system undergoes during combination. The current study provides an example to shed light on the entropy issue in the quark combination model. Acknowledgment. We thank S. Bass, R. Hwa, C.-M. Ko and C.-B. Yang for insightful discussions. ZTL and JS are supported in part by the National Natural Science Foundation of China (NSFC) under the grant 10975092. YXL is supported in part by NSFC under the grants 10425521 and 10675007. FLS is supported by NSFC un- der the grant 10775089. QW is supported in part by the ’100 talents’ project of Chinese Academy of Sciences (CAS) and by the NSFC under the grants 10675109 and 10735040. [1] V. V. Anisovich and V. M. Shekhter, Nucl. Phys. B 55 , 455 (1973). [2] J. D. Bjorken and G. R. Farrar, Phys. Rev. D 9 , 1449 (1974). [3] R. C. Hwa and C. B. Yang, Phys. Rev. C 67 , 034902 (2003). [4] V. Greco, C. M. Ko and P. Levai, Phys. Rev. Lett. 90 , 202302 (2003). [5] R. J. Fries, B. Muller, C. Nonaka and S. A. Bass, Phys. Rev. Lett. 90 , 202303 (2003). [6] V. Greco, C. M. Ko and P. Levai, Phys. Rev. C 68 , 034904 (2003). [7] C. Nonaka, B. Muller, S. A. Bass and M. Asakawa, Phys. Rev. C 71 , 051901 (2005). [8] R. C. Hwa and C. B. Yang, Phys. Rev. C 70 , 024905 (2004). [9] R. C. Hwa, arXiv:0904.2159 [nucl-th]. [10] Q. B. Xie and X. M. Liu, Phys. Rev. D 38 , 2169 (1988). [11] Z. T. Liang and Q. B. Xie, Phys. Rev. D 43 , 751 (1991). [12] Q. Wang and Q. B. Xie, J. Phys. G 21 , 897 (1995). [13] Q. Wang, Z. G. Si and Q. B. Xie, Int. J. Mod. Phys. A 11 , 5203 (1996). [14] F. l. Shao, Q. b. Xie and Q. Wang, Phys. Rev. C 71 , 044903 (2005). [15] J. Song, F. l. Shao, Q. b. Xie, Y. f. Wang and D. m. Wei, arXiv:nucl-th/0703095. [16] C. e. Shao, J. Song, F. l. Shao and Q. b. Xie, Phys. Rev. C 80 , 014909 (2009). [17] E. Schnedermann, J. Sollfrank and U. W. Heinz, Phys. Rev. C 48 , 2462 (1993). [18] N. Demir and S. A. Bass, Phys. Rev. Lett. 102 , 172302 (2009). [19] P. Braun-Munzinger, D. Magestro, K. Redlich and J. Stachel, Phys. Lett. B 518 , 41 (2001). [20] P. Braun-Munzinger, K. Redlich and J. Stachel, arXiv:nucl-th/0304013.