---
title: "QGP Transport Inference Interactive Lab | Sandbox Physics"
description: "How much does a viscosity estimate depend on the initial state?"
canonical_url: "https://sandboxphysics.com/labs/qgp-transport-inference/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/qgp-transport-inference/"
---

FR06 · Conditional Bayesian inference

# QGP Transport Inference

**How much does a viscosity estimate depend on the initial state?** A viscosity estimate depends on the initial geometry and on correlations that do not come from collective flow. The same saved synthetic events give different conditional posteriors when those assumptions change, so a narrow interval alone cannot establish an unconditional QGP viscosity.

Fit one fixed synthetic event sample under different initial geometries and pair backgrounds. Watch the viscosity posterior move and widen as the assumptions change.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The fixed benchmark contains 4,500 synthetic events with exact stored flow-vector statistics. A two-parameter response model predicts pair correlations. The likelihood uses their empirical covariance plus an assigned model discrepancy and uniform bounded priors. Results are conditional teaching posteriors, not a measurement of QGP viscosity.

Reading the fixed synthetic event sample.

Model, units and sources

Natural units are used. The Gaussian density has unit mean squared radius per axis before deformation. Its short-axis direction defines the elliptic emission plane. This is an assigned response calculation, with no transverse fluid solver.

$$
v_n=\kappa_0\varepsilon_n e^{-1.8n^2(\eta/s)/(RT)},\qquad n=2,3
$$

The response coefficient and damping scale are illustrative. Higher harmonics and nonlinear mode coupling are omitted.

[Gardim et al. (2012)](https://arxiv.org/abs/1111.6538v2) · [Bilandzic et al. (2011)](https://arxiv.org/abs/1010.0233v2) · [Bernhard et al. (2019)](https://doi.org/10.1038/s41567-019-0611-8)

Physics tutorial

## QGP Transport Inference

**Background** Fit one fixed synthetic event sample under different initial geometries and pair backgrounds. Watch the viscosity posterior move and widen as the assumptions change.

**Why it matters** A finite-lived cloud leaves particle directions behind. Inferring its viscosity requires a prediction of how its unknown initial shape becomes those directions.

Start with the essentials

- **Focus question**: How much does a viscosity estimate depend on the initial state?
- **One-sentence intuition**: The same particle correlations can favor different viscosities when the initial geometry or pair background changes.

### Core mathematical model

#### Distinct-particle pair correlation

$$
C_n=\frac{|Q_n|^2-M}{M(M-1)},\qquad Q_n=\sum_{j=1}^{M}e^{in\phi_j}
$$

Subtracting multiplicity removes each particle paired with itself. The saved event flow vectors determine every plotted correlation.

#### Four-particle cumulant

$$
c_n\{4\}=\langle\langle4\rangle\rangle-2\langle\langle2\rangle\rangle^2
$$

Four distinct particles contribute to each four-particle term. Cumulants suppress many pair backgrounds; finite samples and clusters that themselves flow still matter.

#### Conditional posterior

$$
p(\eta/s,\kappa_0\mid D,\mathcal M)\propto\exp\!\left[-\tfrac12\Delta^\mathsf T\Sigma^{-1}\Delta\right]p(\eta/s,\kappa_0)
$$

The residual compares the same six observed pair means with the selected model. Marginalizing the response amplitude gives the viscosity interval.

### Common difficulties

#### What the estimate means

**Typical misconception** A narrow posterior fixes the viscosity of real QGP.

**Better mental model** The displayed interval conditions on the chosen response, geometry, priors, and error model. Real extractions also simulate the full collision and compare many observables.

### Run the experiment

1. 01

   #### Keep the sample fixed

   Start with Planted assumptions, then download the event records.

   **What to observe:** The benchmark holds 4,500 events. Its seed and generation parameters travel with the records.

2. 02

   #### Change the initial geometry

   Choose Larger ellipticity and compare the shaded interval.

   **What to observe:** The data points stay put. The model and conditional posterior move.

3. 03

   #### Test the background

   Choose Ignore doublets, then Allow model error.

   **What to observe:** A background change shifts the estimate; a larger discrepancy generally broadens the range compatible with the same sample.

Physical conclusion

Quote the model together with the posterior.

## Related experiments and articles

Heavy-ion matter and hydrodynamics · Reading path

### From directional pressure to transport inference

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Measure common flow through particle correlations**](https://sandboxphysics.com/stories/qgp-hydrodynamics/multiparticle-correlations/)
2. [Article **Infer transport while changing the assumed initial state**](https://sandboxphysics.com/stories/qgp-hydrodynamics/conditional-transport-inference/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)