1.6. Two-state systems Consider a system of N free classical particles. The energy of each particle can take only two values: 0 and E(E > 0). Let n0 and n1 the occupation numbers of the two energy levels and U the total energy of the system.

a. Determine the entropy of the system.

b. Determine n0, n1 and their fluctuations.

c. Express the temperature T as a function of U and show that it can take negative values.

d. Discuss what happens when a system at negative temperature is put in thermal contact with a system at positive temperature.