The pressure of the quark–gluon plasma at zero baryon density

2026-11-05

Notes / Interactive

The pressure of the quark–gluon plasma at μ_B = 0

November 2026 · Interactive

The figure below shows the scaled pressure P/T⁴ of the quark–gluon plasma at vanishing baryon chemical potential, computed in the self-consistent T-matrix approach,¹ for temperatures from 0.15 to 0.40 GeV.

At vanishing baryon chemical potential the other thermodynamic quantities follow from the pressure as a function of temperature:

\[ s = \frac{\partial P}{\partial T}, \qquad \varepsilon = Ts - P, \qquad \frac{\varepsilon - 3P}{T^4} = T\,\frac{\partial}{\partial T}\!\left(\frac{P}{T^4}\right) \]

Move the slider to read off the pressure at a given temperature.

eos = FileAttachment("eos_mu0.csv").csv({typed: true})
viewof T = Inputs.range([0.15, 0.40], {step: 0.005, value: 0.25, label: "Temperature T (GeV)"})

at = {
  const i = eos.findIndex(d => d.T >= T);
  if (i <= 0) return eos[0].old;
  const a = eos[i - 1], b = eos[i];
  return a.old + (b.old - a.old) * (T - a.T) / (b.T - a.T);
}
html`<p class="ms-tabular" style="margin: 4px 0 12px; font-size: 15px;">T = <b>${T.toFixed(3)} GeV</b> · P/T⁴ ≈ <b>${at.toFixed(2)}</b></p>`

css = getComputedStyle(document.body)
tok = name => css.getPropertyValue(name).trim()
Plot.plot({
  width: 680, height: 340, marginLeft: 44,
  style: {fontFamily: "Inter, sans-serif", fontSize: "12px", color: tok("--ms-muted"), background: "transparent"},
  x: {label: "T [GeV]", domain: [0.15, 0.40]},
  y: {label: "P/T⁴", grid: true, domain: [0, 4]},
  marks: [
    Plot.line(eos, {x: "T", y: "old", stroke: tok("--ms-accent"), strokeWidth: 2.5, curve: "monotone-x"}),
    Plot.dot(eos, {x: "T", y: "old", r: 2.5, fill: tok("--ms-accent")}),
    Plot.ruleX([T], {stroke: tok("--ms-ink"), strokeDasharray: "3 4"}),
    Plot.dot([{T, v: at}], {x: "T", y: "v", r: 5, fill: tok("--ms-bg"), stroke: tok("--ms-ink"), strokeWidth: 1.5})
  ]
})

P/T⁴ against T at μ_B = 0, 14 computed temperatures (data set mu0_fit1_rc, old kinematics), joined by a smooth curve.

Over this range P/T⁴ rises from 0.63 at T = 0.15 GeV to 3.59 at T = 0.40 GeV.

[What the curve shows and how it compares with lattice QCD: to be written by the author.]

Use the numbers

The values in this figure as a CSV file (T in GeV, P/T⁴).

Download CSV

Footnotes

1. K. Maslov, R. Rapp, J. Grefa, V. Dexheimer and C. Ratti, Strongly coupled quark matter in neutron stars and their mergers, arXiv:2608.28879.