In Part 4, I presented a nifty result supporting my claim that classical statistical mechanics reduces to thermodynamics when Boltzmann’s constant approaches zero. I used a lot of physics jargon to explain why I care about this result. I also used some math jargon to carry out my argument. This may have been off-putting. But ..read more

In 1596, Kepler claimed that the planetary orbits would only follow “God’s design” if there were two more planets: one between Mars and Jupiter and one between Mercury and Venus. Later folks came up with the Titius–Bode law This says that for each n there should be a planet whose distance from the Sun is ..read more

V. A. Antonov did somes remarkable simulations showing that even in Newtonian mechanics, gravitating systems can violate the usual rules of thermodynamics. Instead of reaching equilibrium they get hotter and hotter! Suppose you put a lot of stars in a large sphere, and suppose (unrealistically) that they bounce elastically off the walls of this sphere ..read more

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant approaches zero. In Part 2, I explained exactly what I mean by ‘thermodynamics’. I also showed how, in this framework, a quantity called ‘negative free entropy’ arises as the Legendre transform of entropy. In Part ..read more

In Part 1, I explained how statistical mechanics is connected to a rig whose operations depend on a real parameter and approach the ‘tropical rig’, with operations and as I explained my hope that if we take equations from classical statistical mechanics, expressed in terms of this -dependent rig, and let we get equations in ..read more

I’m trying to work out how classical statistical mechanics can reduce to thermodynamics in a certain limit. I sketched out the game plan in Part 1 but there are a lot of details to hammer out. While I’m doing this, let me stall for time by explaining more precisely what I mean by ‘thermodynamics’. Thermodynamics ..read more

Besides learning about individual physical theories, students learn different frameworks in which physical theories are formulated. I’m talking about things like this: • classical statics • classical mechanics • quantum mechanics • thermodynamics • classical statistical mechanics • quantum statistical mechanics A physical framework often depends on some physical constants that we can imagine varying ..read more

Physicists like to study all sorts of simplified situations, but here’s one I haven’t seen them discuss. I call it an ‘energy particle’. It’s an imaginary thing with no qualities except energy, which can be any number I hate it when on Star Trek someone says “I’m detecting an energy field” — as if energy ..read more

I keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again. The Bernoulli numbers can be defined like this: and if you grind them out, you get and so on. The pattern is quite strange. Bernoulli numbers ..read more

  Wow — evidence that very massive neutron stars may have cores made of deconfined quark matter! The idea of a ‘quark star’ is not new, but I didn’t know it was a serious possibility. An ordinary neutron star has a core made mostly of densely packed neutrons. A matchbox-sized chunk of this stuff weighs ..read more