We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase space are related to thermodynamic equilibrium and statistical fluctuations in the Boltzmann-Gibbs statistical mechanics. The physical motivation for this analysis rests upon the possibility of having, instead of a direct control of the intensive parameters determining the state of the corresponding physical reservoirs, the control of a set of differentiable functions of the original variables. Likewise, we consider a set of differentiable functions of the extensive variables accounting for the possibility of not having direct access to the original variables. We find that the effect of reparametrizations on the thermodynamic phase space can be codified, in geometrical terms, in its contact and Riemannian structures. In particular, we single out a rank-two tensor that enters in the definition of the metric which geometrically comprises the information about such reparametrizations. We notice that even if these geometric structures are modified by the reparametrizations, the metric structure on the thermodynamic space of equilibrium states is preserved.
Stochastic Thermodynamics on Time-Evolving Curved Spaces
The University of Tokyo（东京大学）；RIKEN Center for Advanced Intelligence Project (AIP)（理化学研究所先进智能项目中心）；Inamori Research Institute for Science (InaRIS)（稻盛科学技术研究所）
Instituto de Matemática e Estatística, Universidade Federal da Bahia（巴伊亚联邦大学数学与统计学院）；Faculdade de Ciências Exatas e Naturais - Departamento de Matemática e Estatística, Universidade do Estado do Rio Grande do Norte（北里奥格兰德州州立大学理学院数学与统计系）
The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations
Università di Torino（都灵大学）；Additati&Partners Consulting s.r.l（Additati&Partners咨询公司）；Tel-Aviv University（特拉维夫大学）；Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）
