# Boltzmann equation

Kinetic theory bridges the gap between the big and the small to understand systems made up of many components: from plasmas to people.

Fields medallist Cédric Villani talks to us about our solar system, chaos, and what it's like being a mathematical superstar.

There's no doubt that information is power, but could it be converted into physical energy you could heat a room with or run a machine on? In the 19th century James Clerk Maxwell invented a hypothetical being — a "demon" — that seemed to be able to do just that. The problem was that the little devil blatantly contravened the laws of physics. What is Maxwell's demon and how was it resolved?

What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.

What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.

**Peter Markowich**is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell.

*Plus*went to see him to find out more, and ended up with a pictorial introduction to partial differential equations.