Rayleigh-Schrödinger Perturbation Theory and Nonadditive Thermodynamics

Area of Science:

• Physical Chemistry
• Quantum Mechanics
• Statistical Thermodynamics

Background:

• Classical thermodynamics accurately describes large systems but fails for smaller ones.
• Terrell L. Hill generalized thermodynamics for small systems, but it lacked quantum mechanical reconciliation.
• Existing frameworks struggle to unify macroscopic thermodynamic properties with microscopic quantum behavior in small systems.

Purpose of the Study:

• To reconcile Hill's generalized thermodynamics with quantum mechanics.
• To develop a thermostatistical approach for small systems consistent with quantum theory.
• To make advanced thermodynamic concepts accessible to physical chemists.

Main Methods:

• Introduced a temperature-dependent perturbation to the particles' energy spectrum.
• Applied a simple thermostatistical analysis to quantum mechanical eigenenergies.
• Demonstrated the recovery of Hill's generalized thermodynamic framework.

Main Results:

• Hill's generalized thermodynamic framework for small systems is recovered.
• The framework is shown to be consistent with a thermostatistical treatment of quantum mechanical eigenenergies.
• A method is presented that bridges classical thermodynamics, quantum mechanics, and small-system behavior.

Conclusions:

• The study successfully reconciles Hill's generalization with quantum mechanics.
• This work provides a more complete and universally applicable thermodynamic theory.
• The findings offer a valuable tool for physical chemists studying diverse systems.