Thermodynamic analysis of autonomous quantum systems

TL;DR

The paper applies an autonomous quantum thermodynamics framework to interacting quantum systems, deriving a second-law form that accommodates energy exchanges as heat, work, and non-unitary exergy across arbitrary coupling. It shows that in the semiclassical limit energy exchanges reduce to local work with a distinct interaction-energy contribution, while in the quantum regime work can arise from population inversion and coherence, and also from a dimension-driven non-unitary channel. Using models such as Jaynes-Cummings and qubit–qubit interactions, the work-heat partition depends on initial states and Hilbert-space dimensionality, with reaction-coordinate mapping clarifying bath energy flows. This framework provides a refined, operational toolkit for energy accounting in realistic quantum devices and guides strategies for energy efficiency in quantum technologies.

Abstract

Traditional quantum thermodynamic frameworks associate work to energy exchanges induced by unitary transformations generated by external controls, and heat to energy exchanges induced by bath interaction. Recently, a framework was introduced aiming at extending the thermodynamic formalism to genuine quantum settings, also referred to as autonomous quantum systems: free from external controls, only quantum systems interacting with each other. In this paper, we apply such a thermodynamic framework to common experimental situations of interacting quantum systems. In situations where traditional frameworks detect only heat exchanges, the recent autonomous thermodynamic framework points at work exchanges based on two mechanisms: population inversion and coherence generation / consumption. Such mechanisms are well known in the literature for being related to work expenditure and extraction, in particular in relation with ergotropy, which emphasizes the relevance of the autonomous framework and the limitations of traditional ones. Furthermore, the autonomous framework also identifies a genuine non-unitary mechanism of work exchange related to athermality. %, also pointed out as a resource for work extraction. Finally, in the semi-classical limit, the autonomous framework identifies all energy exchanges as pure work, but distinguishes between local work and interaction energy. Our results show that the autonomous framework provides a refined analysis of work exchange mechanisms in the quantum realm and serves as a consistent approach to analyze thermodynamic processes in realistic quantum devices.

Figures (13)

• Figure 1: Plot of the internal energy, heat, and work for the qubit (A) and the QHO (B) as functions of the dimensionless time $gt$. All thermodynamic quantities are expressed in units of $\hbar \omega$; this convention is used throughout all subsequent figures. The qubit is initially in the ground state and QMO is initially in a coherent state $\ket{\psi_{HO}}(0) = \ket{\alpha}$. Parameters: $\omega_A = \omega_B$, $\alpha = 30$ and $g = 0.01 \omega_A$.
• Figure 2: Plot of the thermodynamical quantities for both the qubit (A) and the QHO (B), as a function of time . Parameters: $\omega_A = \omega_B$ and $g = 0.01 \omega_A$.
• Figure 3: Plot of the internal energy, heat and work for the qubit and the QHO, as a function of time. The qubit is initially in the state $\ket{\psi_A(0)} = \frac{1}{\sqrt{2}}(\ket{e} + \ket{g})$. Parameters: $\omega_A = \omega_B$ and $g = 0.01 \omega_A$.
• Figure 4: Plot of the thermodynamical quantities for the qubit and the QHO, as a function of time. The qubit is initially in a thermal state $\rho_A(0) = \frac{1}{2}(\ket{g}\bra{g} + \ket{e}\bra{e})$. Parameters: $\omega_A = \omega_B$ and $g = 0.01 \omega_A$.
• Figure 5: Plot of the internal energy, heat and work for both qubits, as a function of time. The qubit A is initially in the excited state, $\ket{e}$ and qubit B is initially in the ground state, $\ket{g}$. Parameters: $\omega_A = \omega_B$ and $g = 0.01 \omega_A$