Neves Luis Rodrigo, Brito Frederico
Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, SP, Brasil.
Quantum Research Centre, Technology Innovation Institute, P.O. Box 9639, Abu Dhabi, UAE.
Sci Rep. 2025 Sep 26;15(1):33175. doi: 10.1038/s41598-025-15833-9.
The quest to develop a general framework for thermodynamics, suitable for the regime of strong coupling and correlations between subsystems of an autonomous quantum "universe," has entailed diverging definitions for basic quantities, including internal energy. While most approaches focus solely on the system of interest, we propose that a universal notion of internal energy should also account for the environment in order to keep consistency with the closed-system energy of the universe. We introduce an abstract framework to describe all effective Hamiltonian-based approaches and address a rigorous definition of energy additivity in this context, in both a weak and a strong form, discussing the underlying subtleties. As an illustration, we study a particular two-qubit universe model, obtaining the exact master equations for both parties and calculating their effective Hamiltonians and internal energies as given by the recently devised minimal dissipation approach. In this case, we show that internal energies are neither additive nor conservative, which leads to unphysical features.
为自主量子“宇宙”的子系统之间的强耦合和关联状态开发一个适用于热力学的通用框架，这一探索导致了包括内能在内的基本量的不同定义。虽然大多数方法仅关注感兴趣的系统，但我们认为，为了与宇宙的封闭系统能量保持一致，内能的通用概念也应该考虑环境。我们引入一个抽象框架来描述所有基于有效哈密顿量的方法，并在这种情况下以弱形式和强形式给出能量可加性的严格定义，讨论其潜在的微妙之处。作为一个例子，我们研究一个特定的两量子比特宇宙模型，得到双方的精确主方程，并计算由最近设计的最小耗散方法给出的有效哈密顿量和内能。在这种情况下，我们表明内能既不可加也不守恒，这导致了不符合物理实际的特征。
