INTERACTIVE MODELFIELD NOTESOFT MATTER PHYSICS

The Cacio e Pepe Phase Bench

A live model accompanying “The Phase Transition Hiding in Your Cacio e Pepe”

Study: Field note
Review: Peer-edited by the club review board
Article: 13 sectionsabout 22 min
Files: LaTeX source28 kB

The published result is a boundary at 1% starch, relative to cheese mass, above a temperature that depends on how much starch is present. Below, drag the starch and temperature sliders yourself and watch which side of the boundary you land on. Then scale the paper's own recipe to whatever batch you actually want to cook, and check where your starch lands on the same axis.

clumps when: starch % < 1% and temperature > boundary(starch %)

Model 1. Cross the boundary yourself

The left panel is the phase diagram: starch concentration on one axis, temperature on the other. The shaded regions follow the paper's reported anchor points — a boundary at about 65 °C with no starch present at all, rising steeply and disappearing off the top of the tested range by 1% starch, with a separate stiff-sauce band starting around 4% — connected here by a smooth interpolating curve that is our own illustration of the boundary's shape, not a redigitization of the paper's measured images. The right panel renders whatever state your two sliders land on: a swirl for a smooth sauce, or curdled clumps for the Mozzarella Phase.

Starch2.5% of cheese massSauce temperature85 °C

Jump to a case from the paper

state: smoothmargin above 1% line: 2.5×

At 2.5% starch, the sauce stays smooth across the whole 50–95℃ range the paper tested.

The rising boundary near 1% and the flat stiff band near 4% follow the paper's reported anchor values [1]; the curve joining them is ours, drawn to illustrate the shape of the effect rather than to reproduce a measured pixel.

Model 2. Scale the recipe and check the arithmetic

The paper's own recipe serves two: 200 g of cheese, 5 g of starch, 150 g of water, 300 g of pasta. Scale it to whatever batch you actually want, and the calculator below keeps every ingredient in the same proportion, converts the starch into teaspoons using a standard kitchen reference (about 2.67 g per teaspoon — our own conversion, not the paper's), and works out the protein mass fraction φ of the cheese-and-water mixture the same way the paper does, using Pecorino Romano's own nutritional value of 27 g protein per 100 g of cheese.

Cheese in your batch200 gYour starch dose2.5% of cheese mass

Batch size presets (paper's recipe = 200g cheese)

Starch needed: 5.0 g
In teaspoons: ≈ 1.9 tsp (our conversion)
Water needed: 150 g ≈ 0.63 cup
Pasta to match: 300 g
Protein fraction φ: 0.154
vs. binodal minimum: 0.020 above φ≈0.134

2.5% sits inside the paper's ideal 2–3% window, 2.5× above the 1% survival line.

Ingredient ratios, the 27 g/100 g protein figure, and the 1%, 2–3% and 4% landmarks are the paper's own [1]. The teaspoon conversion, the cup conversion, and every φ calculation on this page are the club's own arithmetic.

What the sliders make obvious

Two things are easy to say in prose and hard to really feel until you drag a slider. The first is how narrow the unsafe zone actually is in absolute terms: the boundary between reliably smooth and occasionally disastrous is under a single percentage point of starch, which the calculator above turns into well under one teaspoon in a normal home batch. The second is that scaling a recipe by mass, not by clumsy proportional guessing, keeps you at exactly the same point on the phase diagram no matter how many people you are feeding — the starch percentage relative to cheese, and the protein fraction φ, do not move at all as the batch size changes, only the absolute grams do.

Neither model here reruns the paper's actual temperature-ramp experiment; that took Petri dishes, backlighting, and an image-segmentation pipeline the club did not attempt to reproduce. What is here is the reported shape of the phase diagram, and the arithmetic connecting it to a kitchen, left where you can check every number.