Thermodynamic framework for the ground state of a simple quantum system

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Thermodynamics

Background:

• The ground state of a two-level system with a diagonal Hamiltonian follows Boltzmann-Gibbs statistical mechanics and the third law of thermodynamics (zero entropy at zero temperature).
• A perturbation term in the Hamiltonian can alter the system's ground state properties.

Purpose of the Study:

• To investigate the thermodynamic implications of introducing a perturbation with non-zero off-diagonal elements in the Hamiltonian of a two-level system.
• To establish a consistent thermodynamic framework for such perturbed systems.

Main Methods:

• Analysis of a two-level system's Hamiltonian H = H0 + λV, where V has non-zero off-diagonal elements.
• Introduction of an effective temperature (θ) conjugated to the system's entropy (S).
• Formulation of an infinitesimal heat quantity (δQ = θdS) and the first law of thermodynamics.

Main Results:

• A non-trivial ground state with entropy S ≠ SBG is shown to arise from the perturbation.
• An effective temperature θ is introduced, proportional to the perturbation strength (λz).
• A thermodynamic framework, including a Carnot cycle and potentials, is established, analogous to standard thermodynamics with T ↔ θ.

Conclusions:

• Perturbations with non-zero off-diagonal elements in the Hamiltonian lead to significant changes in the ground state thermodynamics of two-level systems.
• The developed framework supports a third law-like behavior for entropy (S → 0 as θ → 0).
• The study provides a new perspective on thermodynamics in quantum systems.