Information Geometry,Phase Space Topology and Renormalisation: An Emergent Space-Time Description of Statistical Mechanics

Panigrahi, Aaditya (2018) Information Geometry,Phase Space Topology and Renormalisation: An Emergent Space-Time Description of Statistical Mechanics. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Aaditya Panigrahi (13M145)) 13M145.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

Classical-Quantum Holonomy is studied in generality. Using 1D Ising Model as the test model, modifications to the Holonomy are, in general suggested. Following this, the boundary sensitive Partition Function for 1D Ising Model, in accordance with the previously suggested modification is calculated, for APBC a barrier wall at h=0 for the energy manifold is obtained. With the inclusion of Twisted Boundary condition, using decimation process, the Renormalisation Equations are derived, using which, the Boundary condition quantisation is illustrated. The Classical and Qauntum System is studied using Information Theory. Symmetry Breaking of the Quantum system is studied using purity, relative entropy, and Fisher Information Metric. A method for geometrisation of Renormalisation is suggested. For this suggestion, the existence of Raychaudhuri Equation is derived.

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