Energy additivity as a requirement for universal quantum thermodynamical frameworks.

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Quantum Information Theory

Background:

• Developing a universal thermodynamic framework for strongly coupled quantum systems is challenging.
• Existing definitions of internal energy often neglect environmental interactions, leading to inconsistencies.
• Autonomous quantum systems require a generalized approach to thermodynamics.

Purpose of the Study:

• To propose a universal definition of internal energy that accounts for environmental interactions.
• To establish a rigorous framework for energy additivity in quantum systems.
• To investigate the properties of internal energy in a specific two-qubit quantum universe model.

Main Methods:

• Introduction of an abstract framework for effective Hamiltonian-based approaches.
• Definition of weak and strong forms of energy additivity.
• Analysis of a two-qubit quantum universe model using the minimal dissipation approach.
• Derivation of exact master equations and calculation of effective Hamiltonians and internal energies.

Main Results:

• Internal energies in the two-qubit model are shown to be neither additive nor conservative.
• The proposed framework allows for a consistent definition of internal energy, including environmental effects.
• The study identifies unphysical features arising from non-additive and non-conservative internal energies.

Conclusions:

• A universal notion of internal energy in quantum thermodynamics must incorporate environmental contributions.
• The minimal dissipation approach reveals non-physical characteristics in simple quantum systems.
• Further research is needed to refine thermodynamic frameworks for complex quantum systems.