Interrelation of Non-Classicality, Entropy, Irreversibility and Work extraction in Open Quantum Systems

TL;DR

This work investigates how non-classicality, entropy, entropy production, and extractable work interrelate in open quantum systems by analyzing both spin–spin and spin–boson models, including collision, central spin, NMAD, GAD, and Jaynes–Cummings dynamics. The authors show a consistent pattern where the non-classical volume $\delta$ evolves in opposition to the von Neumann entropy $S$, while entropy production $\Sigma$ opposes ergotropy $\mathcal{W}$, with reservoir initialization playing a crucial role in shaping these relations. Across models, a universal thermodynamic–informational structure emerges, yet non-Markovianity and bath state can induce desynchronization or preserve correlations depending on the scenario. These findings deepen the link between quantum information resources and open-system thermodynamics and have potential implications for designing energy-efficient quantum technologies and batteries.

Abstract

The interplay of non-classical volume, von Neumann entropy, entropy production, and ergotropy is investigated in various open quantum systems. Two categories of open quantum system models are utilized: spin-spin and spin-boson interaction models. The spin-spin interaction models include the quantum collision and central spin models. On the other hand, the spin-boson interaction models consist of non-Markovian amplitude damping channel, Markovian generalized amplitude damping channel, and the Jaynes-Cummings model. Across these various open quantum systems, universal interrelations emerge, where the non-classical volume shows contrasting evolution with entropy, and entropy production contrasts with ergotropy. The initial state of the reservoir in these open quantum systems is shown to have an impact on these interrelations. These findings establish an interesting link between quantum information and the thermodynamics of open quantum systems.

Figures (6)

• Figure 1: This diagram illustrates a single-qubit collision model in which the system qubit, denoted as $S$, interacts with a sequence of ancilla qubits $R_n$. The spiral lines represent a Heisenberg-type interaction between the system qubit $S$ and the ancillae. In contrast, the double-sided arrowed straight lines indicate a partial-swap interaction between successive ancilla qubits.
• Figure 2: Variation of non-classical volume ($\delta$), von-Neumann entropy ($S$) in subplot $(a)$, and entropy production ($\Sigma$), ergotropy ($\mathcal{W}$) in subplot $(b)$ with the number of collisions of the single-qubit maximally negative quantum state using a non-Markovian collision model. The parameters are: $\omega_s = 1.5$, $\omega_R = 1$, $\beta = 50$, $g_{SR} = 0.5$, $\Theta = 0.98\frac{\pi}{2}$ and $\tau = 0.5$.
• Figure 3: Variation of non-classical volume ($\delta$), von-Neumann entropy ($S$) in subplot $(a)$, and entropy production ($\Sigma$), ergotropy ($\mathcal{W}$) in subplot $(b)$ with time using the central spin model of the single-qubit maximally negative quantum state. The parameters are: $\omega_0 = 1.5$, $\omega = 1$, $\beta = 100$, $\boldsymbol{\epsilon} = 0.5$ and $N = 50$.
• Figure 4: Variation of non-classical volume ($\delta$), von-Neumann entropy ($S$) in subplot $(a)$, and entropy production ($\Sigma$), ergotropy ($\mathcal{W}$) in subplot $(b)$ with time of the single-qubit maximally negative quantum state under the NMAD channel. The parameters are: $\omega_0 = 10$, $\lambda = 0.05$ and $\gamma_0 = 50$.
• Figure 5: Variation of non-classical volume ($\delta$), von-Neumann entropy ($S$) in subplot $(a)$, and entropy production ($\Sigma$), ergotropy ($\mathcal{W}$) in subplot $(b)$ with time of the one-qubit maximally negative quantum state. The evolution is governed by the Markovian generalized amplitude damping master equation. The parameters are: $\omega_0 = 1.5$, $\beta = 1$, and $g = 0.05$.