Canonical Quantization for Equilibrium Thermodynamics

• Grant number: 24/08114-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2025
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Bárbara Lopes Amaral
• Grantee: Luis Felipe Santos da Silva
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/06454-7 - Non-locality and contextuality as resources for quantum information, quantum computation and the certification of quantum devices, AP.JP

Abstract

The present project aims to establish a quantum theory of Equilibrium Thermodynamics through quantization processes analogous to those of Dirac for Analytical Mechanics. This is motivated by the fact that the Thermodynamic formalism can be written under a phase space structure, similar to the case of systems described via Lagrangian and Hamiltonian formalisms, with the nuance that, for this, we need an odd number of canonical variables when attempting to describe a physical system, corroborating the use of Dirac's constrained systems theory. Given that quantization processes for constrained mechanical systems are known, the idea of this work is to mimic it for Equilibrium Thermodynamics, thus mapping the latter into a theory of quantum nature. Therefore, it is expected that quantities such as heat, work, temperature, and entropy will gain precise quantum analogues, so that it is also possible to justify thermodynamic uncertainty relations analogously to the usual uncertainty relations of Quantum Mechanics.