Thermodynamical path integral and emergent symmetry

Area of Science:

• Quantum Many-Body Physics
• Quantum Thermodynamics
• Statistical Mechanics

Background:

• Investigating quantum many-body systems requires understanding their behavior under external control.
• Thermodynamic quantities are crucial for describing system evolution, especially in isolated systems.
• Path integral formulations offer a powerful framework for analyzing time evolution.

Purpose of the Study:

• To formulate a path integral for the time evolution of a quantum many-body system under external parameter control.
• To derive an effective action for thermodynamic entropy and its conjugate variable in quasistatic operations.
• To identify symmetries and invariants within this quantum thermodynamic framework.

Main Methods:

• Formulation of a path integral over thermodynamic state space trajectories.
• Derivation of an effective action for thermodynamic entropy and its conjugate variable.
• Analysis of symmetries emerging from the path integral for quasistatic processes.

Main Results:

• The propagator is described by thermodynamic quantities under specific assumptions.
• An effective action for thermodynamic entropy and its conjugate variable is derived.
• A symmetry related to the uniform translation of the conjugate variable emerges in the path integral.

Conclusions:

• Thermodynamic entropy is identified as a Noether invariant in quantum mechanics.
• The derived symmetry provides a new perspective on conservation laws in quantum systems.
• This work bridges quantum mechanics and thermodynamics through path integral formalism.