Dork Scratchings

Is it possible to bring a temperature below absolute zero? And if so, what does, say, -1K look like? Surprisingly, negative temperatures are in fact possible, but only in some circumstances. To understand how, we need to get a better idea of what temperature actually means from a statistical thermodynamics point of view. Suppose you have a system of $N$ particles$^{\dagger}$, each of which can have an energy level from a discrete list $$ 0 < E_1 < E_2 < E_3 < ... $$ Now suppose that there are $N_1$ particles in state $E_1$, $N_2$ in $E_2$ and so on. Using combinatorics$^{\dagger_2}$ we can see that the number of ways this particular configuration can be achieved is given by $$ \Omega = \frac{N!}{N_1!N_2!N_3!...} $$ The next question is: if we know the total energy of the system $E_{total}$ can we work out the distribution of particles across the energy states? Well, we know the most likely distribution is that which can be achieved in the greatest number of ways. I.e. we...

Why do we experience time the way we do?  The future seems a very different beast to the past, but as far as we can tell all of nature's fundamental laws are fully reversible.  Take a ball that's just been kicked into the air.  Newton tells us that the ball will lose speed as it rises to it's greatest height at which point it will start to fall and that it will trace out a parabola as it does.  However, if we play the video backwards, the ball will do exactly the same thing,   and this is   because the laws apply equally well when you start with "final" conditions instead of "initial" conditions and rewrite the equations in terms of "backwards time" $\tau = -t$ instead of time $t$. Despite this we do not experience the two directions the same.  In this post I will give an argument for why this is the case - one that borrows from thermodynamics, Hamiltonian classical mechanics, and Landauer's Limit. Phase Space and Entropy The 19th Century I...

When the 2nd law of thermodynamics was discovered a lot of theorists were understandably suspicious.  It said that entropy always increases with time, or $\frac{dS}{dt} > 0$, but this seems to go against time reversal symmetry, which is a feature of all physical laws. (Okay... in QM you also have to reverse charge and parity in the system too....)  Amongst those who challenged the new theory was James Clerk Maxwell (he who shed light on light) and he did so with a thought experiment.  Imagine you have a box full of air at a given temperature, and it is divided into two parts.  Between the two is a little door which can be opened and shut by a daemon.  This daemon watches the air molecules speeding towards the door and if the molecule is faster than average and on the LHS he opens the door briefly to let it pass through to the right hand side.  Conversely if the molecule is slower than average and on the RHS the daemon will open the door to let is...