Consider a system of N free particles in which the energy of each particle can assume two and only two distinct values, 0 and E (E>0). Denote by n0 and n1 the occupation numbers of the energy level 0 and E, respectively. The total energy of the system is U. a) Find the entropy of such a system b) Find the most probable values of n0 and n1, and find the mean square fluctuations of these quantities

Consider a system of N free particles in which the energy of each particle can assume two and only two distinct values, 0 and E (E>0). Denote by n0 and n1 the occupation numbers of the energy level 0 and E, respectively. The total energy of the system is U. a) Find the entropy of such a system b) Find the most probable values of n0 and n1, and find the mean square fluctuations of these quantities

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Question

Consider a system of N free particles in which the energy of each particle can assume two and only two distinct values, 0 and E (E>0). Denote by n₀and n₁the occupation numbers of the energy level 0 and E, respectively. The total energy of the system is U.

a) Find the entropy of such a system

b) Find the most probable values of n₀and n₁, and find the mean square fluctuations of these quantities.

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