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Generalized definition of the isothermal compressibility in ( $2 + 1$ )-flavor QCD

D. A. Clarke ¹, J. Goswami ², F. Karsch ², and P. Petreczky ³

¹Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, USA
²Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany
³Physics Department, Brookhaven National Laboratory, Upton, New York, USA

Phys. Rev. D 113, 034502 – Published 10 February, 2026

DOI: https://doi.org/10.1103/xdyq-hphf

Abstract

We introduce a generalized definition of the isothermal compressibility ( $κ_{T, σ_{Q}^{2}}$ ) 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 $κ_{T, σ_{Q}^{2}} = 13.8 (1.3) {fm}^{3} / GeV$ at $T_{pc, 0} = 156.5 (1.5) MeV$ and ${\hat{μ}}_{B} = 0$ . This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons ( $N_{ch}$ ) by the total number of hadrons ( $N_{tot}$ ) at freeze-out. Normalizing this result with the QCD pressure ( $P$ ) we find that the isothermal compressibility on the pseudocritical line stays close to that of an ideal gas, i.e., $P κ_{T, σ_{Q}^{2}} ≃ 1$ .

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Phys. Rev. D 113, 034502– Published 10 February, 2026

Vol. 113, Iss. 3 — 1 February 2026

Received 6 July 2025
Accepted 22 December 2025

DOI: https://doi.org/10.1103/xdyq-hphf

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Generalized definition of the isothermal compressibility in ( $2 + 1$ )-flavor QCD

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

Abstract

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References (33)

Generalized definition of the isothermal compressibility in ( $2 + 1$ )-flavor QCD