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bio website nathanielvirgo.com
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I'm a post-doctoral researcher with a wide range of interests. My career is in complex systems science (or maybe cybernetics) and the origins of life, but I also have research interests in

  • the foundations of statistical mechanics and its relationship to information theory
  • Earth systems science
  • non-equilibrium thermodynamics in general

I'm also generally interested in the foundations of quantum mechanics and in black holes, though I wouldn't say I'm an expert on those things.

It's probably worth noting that despite the fact that my research is in physics-related areas, all my degrees are in other subjects. If I occasionally seem to start talking in an alien language, this is probably why.


Oct
9
reviewed Approve A naive question on the $U(1)$ gauge transformation of electromagnetic field?
Oct
9
comment If I jump will I land in the same spot?
@PrimeWaffle If you hovered in a helicopter (or any other hovering device), you would be exerting an additional force to counteract gravity, the amount you would move relative to the Earth would be highly dependent on the direction and magnitude of this force.
Oct
8
reviewed Edit Is matter a continuous part of the field of space-time?
Oct
8
revised Is matter a continuous part of the field of space-time?
fixed formatting
Oct
8
comment Is matter a continuous part of the field of space-time?
Related (about a different quote by Einstein on the same subject): physics.stackexchange.com/q/77525 - FWIW I think this question is better than that one, because the longer quote means we don't have to speculate as much about the context.
Oct
8
comment Grand canonical ensemble with interaction, simulation doubts
I'm sorry for the short-ish answers - I'm happy to refine them if you have any questions.
Oct
8
answered Grand canonical ensemble with interaction, simulation doubts
Oct
8
comment Definition of phase transitions in statistical mechanics
@gatsu I'm starting to think you're right. I think I'm quite confused about the differences between first- and second-order transitions. I assumed that the critical behaviours would be broadly similar between the two, but as I read more about the subject it seems the "interesting" behaviours are largely confined to second-order transitions. (Though freezing water is first-order and involves breaking rotational symmetry.) I guess the challenge now is to see if I can make a model along these lines that has a second-order transition.
Oct
8
comment Definition of phase transitions in statistical mechanics
@user10001 you might be interested in the update as well. The new version of the model has many microscopic states, rather than just two.
Oct
8
comment Definition of phase transitions in statistical mechanics
@Jonas I've updated the question with a version of the model that has a non-zero (positive) transition temperature.
Oct
8
revised Definition of phase transitions in statistical mechanics
pointed out that the change in the addendum is worth paying attention to
Oct
8
comment Definition of phase transitions in statistical mechanics
Many thanks for your helpful comments. I've updated my question with a part about the positive-$T$ transition case, although it's mostly just what you already wrote here. Could you say a little bit more about the relationship to "superselective particles"? I'm not familiar with those.
Oct
8
revised Definition of phase transitions in statistical mechanics
added addendum about a version with a positive transition temperature.
Oct
7
comment Definition of phase transitions in statistical mechanics
@user10001 as an aside though, I should mention that quantities like $Z$ can retain their thermodynamic interpretation even for small systems if you take care to interpret them in the right way. (You just can't get phase transitions.) A lot of the most celebrated recent results in stat mech (the fluctuation theorems, Jarzynski's equality etc.) rely on this.
Oct
7
comment Definition of phase transitions in statistical mechanics
@gatsu $\beta=1/(k_B T)$ is the inverse temperature (standard use in statistical mechanics), and $\lambda$ is a parameter that corresponds to the size of the system, e.g. its volume. Taking the limit of infinite system size is usual (and necessary) in showing that more sophisticated models have phase transitions. In this system it happens that the transition occurs at $\beta=0$, which does correspond to infinite $T$, though I don't see this as a problem for the point I'm making. As I mentioned to Jonas, there's a way to make the transition temperature finite, so I'll update the question later.
Oct
7
comment Definition of phase transitions in statistical mechanics
@user10001 that's certainly true. However, it's not clear that I can't do something trivial like take $10^{23}$ independent copies of this system, which would give me a system with a macroscopic number of states that exhibits the same behaviour. I need to think about this more though.
Oct
7
comment Definition of phase transitions in statistical mechanics
@Jonas though it's worth noting that in order for the transition temperature to be independent of the scale parameter, the degeneracy of the states has to increase exponentially with $\lambda$. This might actually provide some kind of clue about how this model relates to less trivial ones. (I'll edit these observations into the question later.)
Oct
7
comment Definition of phase transitions in statistical mechanics
@Jonas well spotted - but that can be changed by making the states degenerate. If there are several states with $E=0$ and fewer (or just one) with $E=\varepsilon\lambda$, then the transition temperature is positive. I didn't explain that in the question because I wanted to present the simplest example.
Oct
7
revised Definition of phase transitions in statistical mechanics
added 256 characters in body
Oct
7
asked Definition of phase transitions in statistical mechanics