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$$p_i = frac{ expleft(-frac{epsilon _i}{k_BT} right)}{Z} $$ $$ Z= sum_{i} expleft(-frac{epsilon _i}{k_BT} right)$$ A) Is $p_i$ the probability of the system having an energy equal to $epsilon_i$ ? (Probability to be in any of the many microstates that have energy $epsilon_i$ ). B) Or is $p_i$ the probability of the system being in one particular microstate which happens to have energy $epsilon_i$ ? (This microstate is not the only microstate with the same energy). If A) is correct then: $$ Z= sum_{epsilon_i} expleft(-frac{epsilon _i}{k_BT} right)$$ If B) is correct then: $$ Z= sum_{epsilon_i} Omega_iexpleft(-frac{epsilon _i}{k_BT} right),$$ where $Omega_i$ is the multiplicity of the macrostate of energy $epsilon_i$ . From the derivation of the Boltzmann distribution I am inclined to understand it as B)...