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# Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions

## Abstract

Collisions between heavy atomic nuclei at ultrarelativistic energies are carried out at particle colliders to produce the quark–gluon plasma, a state of matter where quarks and gluons are not confined into hadrons, and colour degrees of freedom are liberated. This state is thought to be produced as a transient phenomenon before it fragments into thousands of particles that reach the particle detectors. Despite two decades of investigations, one of the big open challenges1 is to obtain an experimental determination of the temperature reached in a heavy-ion collision, and a simultaneous determination of another thermodynamic quantity, such as the entropy density, that would give access to the number of degrees of freedom. Here, we obtain such a determination, utilizing state-of-the-art hydrodynamic simulations2. We define an effective temperature, averaged over the spacetime evolution of the medium. Then, using experimental data, we determine this temperature and the corresponding entropy density and speed of sound in the matter created in lead–lead collisions at the Large Hadron Collider. Our results agree with first-principles calculations from lattice quantum chromodynamics3 and confirm that a deconfined phase of matter is indeed produced.

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## Data availability

The data represented in Figs. 2 and 3 are available as Source Data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

F.G.G. was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq grant 205369/2018-9 and 312932/2018-9). M.L. acknowledges support from FAPESP projects 2016/24029-6 and 2017/05685-2. F.G.G. and M.L. acknowledge support from project INCT-FNA Proc. No. 464898/2014-5 and G.G., M.L. and J.-Y.O. from USP-COFECUB (grant Uc Ph 160-16, 2015/13).

## Author information

Authors

### Contributions

F.G.G. and G.G. initiated the project and designed the figures. G.G. devised the initial conditions of the hydrodynamic calculations. F.G.G. carried out the hydrodynamic calculations. M.L. suggested the definitions of the effective temperature and effective volume. J.-Y.O. supervised the project and wrote the manuscript.

### Corresponding author

Correspondence to Jean-Yves Ollitrault.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Sándor Katz and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Source data

### Source Data Fig. 2

Text file containing the values plotted on the figure.

### Source Data Fig. 3

Text file containing the values plotted on the figure.

## Rights and permissions

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Gardim, F.G., Giacalone, G., Luzum, M. et al. Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions. Nat. Phys. 16, 615–619 (2020). https://doi.org/10.1038/s41567-020-0846-4

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• ### Effective (kinetic freeze-out) temperature, transverse flow velocity, and kinetic freeze-out volume in high energy collisions

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Nuclear Science and Techniques (2020)

• ### Recent development of hydrodynamic modeling in heavy-ion collisions

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