Bel-Hadj-Aissa Ghofrane, Gori Matteo, Penna Vittorio, Pettini Giulio, Franzosi Roberto
Dipartimento di Scienze fisiche, della Terra e dell'ambiente (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy.
Quantum Biology Lab, Howard University, 2400 6th St NW, Washington, DC 20059, USA.
Entropy (Basel). 2020 Mar 26;22(4):380. doi: 10.3390/e22040380.
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ϕ 4 models with either nearest-neighbours and mean-field interactions.
在本工作中，我们讨论了如何从相空间子集的几何性质推导热力学可观测量的函数形式。所考虑的几何量主要是所研究系统哈密顿量能级集的外在曲率。特别地，结果表明，热力学可观测量在相变点的特殊行为源于相空间中能级集几何的更基本变化。更具体地说，我们讨论了在具有最近邻和平均场相互作用的ϕ4模型的特殊情况下，相变的微正则描述和几何描述是如何形成的。
