On Earth, electrons are mainly well-behaved creatures. Under extreme conditions – the kind you find in a white dwarf star, say, or in the chamber of a fusion reactor – they fall into a degenerate state, and their behaviour is entirely another matter.

By creating a better model of electrons in one of these degenerate states – called “warm dense matter” – physicists have opened the way to a better understanding of some extreme corners of the universe.

“This is the beginning of a new field of computational science,” says Matthew Foulkes of Imperial College London, who developed the model with colleagues at the University of Kiel, in Germany, and the Los Alamos and Lawrence Livermore national laboratories in the US.

Electrons, the familiar tiny charged particles that flow through wires to produce an electric current, are quite well understood under everyday conditions. Physicists can predict their behaviour both at very small scales (in orbit around an atomic nucleus, say) and very large (the aforementioned electric currents).

However, at very high temperatures (often in the tens of thousands of degrees) and under great pressure, their behaviour becomes fuzzier and ruled by arcane laws of quantum mechanics.

The equations that describe their behaviour in this state are extremely complex and up till now no one has found an exact solution.

Foulkes says it took five years to develop the new techniques necessary to describe warm dense matter accurately.

The result is a complete description of the thermodynamic properties – the relationships between energy, temperature, pressure and polarisation – of electrons in a warm-dense-matter state.

The new model, written up in a paper in Physical Review Letters and published online as freely available computer code, will enable other scientists to improve their understanding in a range of extreme situations such as inside stars and planets, in laser laboratories and in the quest for contained nuclear fusion reactions.