I haven’t heard about thermodynamic computing before, but it sounds pretty interesting. As IEEE Spectrum explains , “the components of a thermodynamic chip begin in a semi-random state. A program is fed into the components, and once equilibrium is reached between these parts, the equilibrium is read out as the solution. This computation style only works with applications that involve a non-deterministic result … various AI tasks, such as AI image generation and other training tasks, thrive on this hardware.” It sounds almost like quantum computing to my layperson ears. [edit: fixed link]
It does sound cool, though I’ve never heard of some of those things.
Monte Carlo methods are where you use randomness to simulate complex problems that are hard to model exactly.
As a simple case let’s say you didn’t konw the value of π, but you were able to generate random numbers really quickly. If you make a square of side d, draw a circle inside, and then randomly place points in the square, then you can calculate
π = percent in circle.A more complex use would be apply the same idea to things like modelling wild fires. If you could generate tons of plausible scenarios then you can determine the most likely routes a forest fire will take.
These methods are used a lot in epidemiology, nuclear physics, astrolonomy, etc.