Cl1mate comput1ng between b1ts and bγtes.

March 15, 2021

Turbulent confetti

To diffuse or not to diffuse

Turbulent confetti

Diffusion or no diffusion

Particle advection is like dumping tea crumps in hot water and whirling them around. If you stir the tea, the little particles get moved around by the flow, but they technically don't mix. Diffusion, an important physical mechanism, is missing. It would be absolutely possible to reverse the tea particle "mixing" and put all the little crumps back to where they were before you started stirring.

However, if you try the same with milk then the milk gets mixed with the tea and you won't be able to separate tea from milk again. So diffusion is not reversible, and actually if you've ever seen a movie of diffusion played in reverse your brain tells you immediately that something is wrong. That's because our brain has implicitly learned the 2nd law thermodynamics, although you may not know what it means. For our tea it means that you could (theoretically) stirr the tea such that the particles move back to where they came from. One probably would need to be quite good in stirring though, but nevertheless. In a sense, for particle advection you can revert time without violating other laws of physics.

What happens when we add diffusion? Well a particle has a certain position, there's (unless you stirr too hard) no dilution of the particles. So it's either here or there but not half a particle here and another quarter there. And that's exactly the underlying problem of why diffusion is not reversible. Imagine you add milk, stirr and then measure that somewhere in the tea there's a droplet with 50% milk and 50% tea, let's call this a concentration of 0.5. You don't know whether it was created from mixing two droplets of concentrations 0 and 1 (as (0.5+0.5)/2 = 0.5) or whether one was 100% milk the other one 0% tea (i.e. (1+0)/2=0.5), or, or, or. There's many ways you could end up with such a milk concentration. So this information is lost due to diffusion.