Energy additivity as a requirement for universal quantum thermodynamical frameworks

TL;DR

This paper proposes a universal definition of internal energy in quantum thermodynamics that accounts for environment interactions, examines energy additivity, and demonstrates issues with non-additivity in a two-qubit model.

Contribution

It introduces an abstract framework for energy additivity in quantum thermodynamics and analyzes its implications in a specific two-qubit universe model.

Findings

Internal energies are neither additive nor conservative in the studied model.

The framework highlights subtleties in defining energy additivity under strong coupling.

Non-additivity leads to unphysical features in quantum thermodynamic descriptions.

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.