極大熵計算理論(Maximum entropy theory)成功的被運用在連結熱容量的實驗數據與能量（焓）的機率分佈後，我們可以輕易的從單純的物理實驗數據，去了解一個物理系統的相狀態。這一套理論，將會有很大的發展空間，而同樣若我們運用在體積分佈，密度分佈更是有很大的發展性及潛在價值。 我們這篇論文貢獻，是發展出高次係數的規則，才有辦法更詳盡的描述難以分辨的共存狀態，並以幾個實驗數據證實高次的重要性。 In statistical mechanics the canonical ensemble theory has been widely used to study the thermodynamic properties of a physical system. Central to this kind of theory is the canonical partition function. Experience shows that an analytical evaluation of the partition function is by no means easy especially for complex systems. An alternative approach within the same theoretical framework is to start with the inverse Laplace transform of partition function. For although this approach to the statistical thermodynamics is no less simpler, the method has the salient traits of resorting to experimental data to extract useful physical quantities. In this work, we re-visit this so-called energy or enthalpy distribution theory. The main advantage in this kind of theory is that, in conjunction with the maximum entropy theory, the energy or enthalpy distribution function can be obtained by resorting only to experimental thermal data. The calculated distribution function can provide insight into the physical system under studied. We illustrate the power of the distribution theory by studying a few selected physical systems.