A generalized definition of the isothermal compressibility in (2+1)-flavor QCD

Abstract: We introduce a generalized definition of the isothermal compressibility ($\kappa_{T,\sigma_Q^2}$) calculable by keeping net conserved charge fluctuations rather than total number densities constant. We present lattice QCD results for this isothermal compressibility, expressed in terms of fluctuations of conserved charges that are related to baryon ($B$), electric charge ($Q$) and strangeness ($S$) quantum numbers. This generalized isothermal compressibility is compared with hadron resonance gas model calculations as well as with heavy-ion collision data obtained at RHIC and the LHC. We find $\kappa_{T,\sigma_Q^2}=13.8(1.3)$~fm$^3$/GeV at $T_{pc,0}=156.5(1.5)$~MeV and $\hat{\mu}B=0$. This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons ($N{\rm ch}$) by the total number of hadrons ($N_{\rm tot}$) at freeze-out. Normalizing this result with the QCD pressure ($P$) we find that the isothermal compressibility on the pseudo-critical line stays close to that of an {\it ideal gas}, {\it i.e.} $P \kappa_{T,\sigma_Q^2}\simeq 1$.