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.

超相对论能量在重原子核之间发生碰撞，从而产生了夸克-胶子等离子体，这是一种物质状态，其中夸克和胶子不局限在强子中，并且颜色自由度得以释放。该状态被认为是瞬态现象，然后分解成数千个到达粒子检测器的粒子。尽管二十年的调查中，大开放的挑战之一¹是获得在重离子碰撞中达到的温度，并同时确定其他热力学量，比如熵密度的实验测定，这将提供访问自由度的数量。在这里，我们利用最先进的流体动力学模拟获得了这样的结论²。我们定义了一个有效温度，该平均温度是在介质的时空演化过程中平均得出的。然后，使用实验数据，我们确定在大型强子对撞机中铅与铅碰撞中产生的物质中的温度以及相应的熵密度和声速。我们的结果与晶格量子色动力学³的第一性原理计算相符，并证实确实产生了限定相。