Simulating quantum thermodynamics of a finite system and bath with variable temperature

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• Simulating quantum systems requires accurate environmental modeling.
• Infinite quantum baths are standard but may not reflect real-world finite systems.
• Understanding finite-size effects is crucial for accurate quantum simulations.

Purpose of the Study:

• To construct and analyze a finite quantum bath with variable temperature.
• To investigate heat flow and equilibrium in quantum thermodynamic simulations.
• To explore deviations from standard thermodynamic relations in finite quantum environments.

Main Methods:

• Development of a finite bath model using non-identical harmonic oscillators.
• Simulation of time evolution for an initial system-environment (SE) pure state.
• Analysis of system-environment microcanonical temperature and energy-temperature relations.

Main Results:

• A time-varying system-environment microcanonical temperature (TSE(t)) was defined.
• The quantum state evolved towards a thermal-like equilibrium state.
• Significant deviations from infinite bath energy-temperature relations and Einstein quantum heat capacity were observed.
• Finite baths exhibited systematically higher temperatures for a given energy compared to infinite baths.

Conclusions:

• Finite quantum baths exhibit unique thermodynamic behaviors distinct from infinite baths.
• Observed finite-size effects may be relevant for small molecules in computational and experimental settings.
• The study provides a framework for more realistic quantum thermodynamic simulations.