Maximum-entropy calculation of energy distributions

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Abstract
We use the maximum-entropy method to calculate molecular energy distributions from the moments of the distribution which in turn can be obtained from the temperature dependence of the heat capacity. If one knows the temperature expansion of the heat capacity through the nth power of the temperature, this then gives the exact first (n+2) energy moments. We illustrate the method for the ideal gas (the Maxwell–Boltzmann distribution of kinetic energy) and then use a model function to show that if one knows four or more moments of the energy distribution this allows one to resolve two or more distinct peaks in this function. We examine argon above the critical pressure, a one-dimensional model, and the protein barnase, all of which exhibit bimodal energy distributions.