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We investigate the speed of sound and polytropic index of quantumchromodynamics (QCD) matter in the full phase diagram based on a 3-flavorPolyakov-looped Nambu-Jona-Lasinio (pNJL) model. The speed of sound andpolytropic index in isothermal and adiabatic cases all have a dip structure atthe low chemical potential side of the chiral phase transition boundary, andthese quantities reach their global minimum values at the critical endpoint(CEP) but are not completely zero, where the values in adiabatic are lightlygreater than those in isothermal. Different from the speed of sound, thepolytropic index also exists a peak around the chiral phase transitionboundary. Along the hypothetical chemical freeze-out lines, the speed of soundrapidly decreases near the CEP, followed by a small spinodal behavior, whilethe polytropic index, especially in isothermal, exhibits a more pronounced andnearly closed to zero dip structure as it approaches the CEP.

Speed of sound and polytropic index in QCD matter