Energy additivity as a requirement for universal quantum thermodynamical frameworks
arXiv:2408.04111 · doi:10.1038/s41598-025-15833-9
Abstract
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 forms, 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.
13 pages, 1 figure. [V2] Sections II and III swapped, with corresponding adaptations, including abstract. Concept of EHR formalized as Definition 1. No-go result included (Proposition 1). Minor changes through the text. [V3] Introduction rewritten. Subsection IIC expanded, now Section III. References 45-50 added. Minor changes through the text, including abstract. [V4] Journal ref in metadata
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