Exercise 12.2: The Boltzmann distribution

1. Add a subroutine to your program to compute the probability distribution $P(E_d)$ of finding the demon with a particular energy. Plot the logarithm of $P(E_d)$ vs. $E_d$ and verify the form (113) for the Boltzmann distribution. What is the slope of the plot? Choose units such that $k_B=1$ and estimate the corresponding magnitude of $T$. Choose the same parameters that were used in the previous exercise.

2. Determine the magnitude of $T$ from the relation (114). Are the two estimates consistent?

3. Compare the value of $T$ obtained in the previous two parts with the value of $T$ found in Exercise 12.1 using the kinetic definition of the temperature. Is the demon in thermal equilibrium with its heat bath?