Role of closed paths in the path integral approach of statistical thermodynamics

4th International Workshop on Statistical Physics and Mathematics for Complex Systems

物理学;数学

Badiali, Jean-Pierre^1,2

Université Pierre et Marie Curie, 4 Place Jussieu, Paris Cedex 05

75230, France^1

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine^2

关键词: Arbitrary functions;    Canonical transformation;    Co-ordinate system;    Equilibrium properties;    Equilibrium state;    Euclidean coordinates;    Microscopic levels;    Path integral approach;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/604/1/012002/pdf
DOI  :  10.1088/1742-6596/604/1/012002

来源: IOP

【 摘 要 】

Thermodynamics is independent of a description at a microscopic level consequently statistical thermodynamics must produce results independent of the coordinate system used to describe the particles and their interactions. In the path integral formalism the equilibrium properties are calculated by using closed paths and an euclidean coordinate system. We show that the calculations on these paths are coordinates independent. In the change of coordinate systems we consider those preserving the physics on which we focus. Recently it has been shown that the path integral formalism can be built from the real motion of particles. We consider the change of coordinates for which the equations of motion are unchanged. Thus we have to deal with the canonical transformations. The Lagrangian is not uniquely defined and a change of coordinates introduces in hamiltonians the partial time derivative of an arbitrary function. We have show that the closed paths does not contain any arbitrary ingredients. This proof is inspired by a method used in gauge theory. Closed paths appear as the keystone on which we may describe the equilibrium states in statistical thermodynamics.