Commit 181a56e7 authored by Michael Wimmer's avatar Michael Wimmer
Browse files

clarify specific heat

parent 518d247e
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......@@ -136,11 +136,13 @@ However, as derived by [Lebowitz](https://journals.aps.org/pr/abstract/10.1103/P
it can be calculated from fluctuations in the kinetic energy instead:
$$
\frac{\langle \delta K^2 \rangle}{\langle K \rangle^2} = \frac{2}{3N}
\left(1-\frac{3N}{2 C_V}\right)
\left(1-\frac{3N}{2 C_V}\right) = \frac{2}{3N}
\left(1-\frac{3}{2 c_V}\right)
$$
where $K$ is the kinetic energy, and $\langle\delta K^2\rangle=
\langle K^2 \rangle - \langle K \rangle^2$ the fluctuations of the
kinetic energy.
kinetic energy. In this formula $C_V$ is the total specific heat capacity
for all $N$ atoms, whereas $c_V=C_V/N$ is the specific heat per atom.
#### Diffusion
......@@ -179,4 +181,4 @@ if you want to observe these different types of behaviour.
- Implement the initialization of positions onto an fcc lattice.
- Show that the initial velocities obey a Maxwell-Boltzmann distribution.
- Perform the rescaling of temperature and show how the desired temperature is attained after a certain amount of rescaling and equilibrating.
- Study at least one observable, and compare its behaviour to literature.
\ No newline at end of file
- Study at least one observable, and compare its behaviour to literature.
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