Abstract

While for closed systems maximum quantum work extraction is given by the ergotropy, this question is
unclear in systems interacting with an environment. First approaches relied on weak-coupling assumptions
[1], and, later, at arbitrary coupling the concept of local ergotropy was proposed [2] as the maximum
extractable work from the system-environment compound by applying a local unitary on the system.  
Being interested in potential connections with many-body phenomena beyond the Markov approximation, in
[3] we start by investigating a two-qubit multimode Rabi model focusing on local ergotropy within a parameter
regime where a Berezinskii-Kosterlitz-Thouless dissipative phase transition occurs [4]. We define a protocol
for charging, storing in quasi-decoherence free subspaces, and discharging the two-qubit system, interpreted
as the working principle of an open quantum battery. We further examine the impact of the phase transition
on local ergotropy and identify potential markers based on it.  
From a more fundamental point of view, we unfold formal weaknesses in the definition of local ergotropy,
such as the fact that it is not guaranteed to be non-increasing in time. We then introduce the concept of
extended local ergotropy [5] by exploiting the free-evolution of the system-environment compound. At
variance with the local ergotropy, the extended local ergotropy is greater by construction, is non-increasing in
time, and activates the potential of work extraction in many cases. We provide examples based on the
Jaynes-Cummings model, presenting practical protocols and analytic results that serve as proof of principle
for the aforementioned advantages.  
We finally shift our attention to a quantum battery made up of many interacting sub-systems and study the
maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting
functional parallel ergotropy (PE) [6] and we devise methods to computing and bounding it. This paves the
way for more realistic and feasible work-extraction protocols, if compared with those that require global
operations on the multipartite system. Focusing on the bipartite case, we first observe that PE outperforms
work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum
available work and the second agent B, subsequently, extracts what is left on the other part. For the agents,
this showcases the need of cooperating for an overall benefit. Notably, the corresponding parallel capacity
can detect entanglement and extending the concept of PE by leveraging system’s free-time evolution allows
one to saturate the gap with the ergotropy of the whole system.
References
[1] D. Farina, et al., “Charger-mediated energy transfer for quantum batteries: An open-system approach”,
Phys. Rev. B 99, 035421 (2019).  
[2] R. Salvia, G. De Palma, and V. Giovannetti, “Optimal local work extraction from bipartite quantum systems
in the presence of Hamiltonian couplings”, Phys. Rev. A 107, 012405 (2023).  
[3] G Di Bello, D. Farina, D. Jansen, C. A. Perroni, V. Cataudella, and G De Filippis, “Local ergotropy and its
fluctuations across a dissipative quantum phase transition”, Quantum Science and Technology 10, 015049
(2024).  
[4] G. De Filippis, et al., “Signatures of dissipation driven quantum phase transition in Rabi model”, Phys. Rev.
Lett. 130, 210404 (2023).  
[5] R. Castellano, D. Farina, V. Giovannetti, and A. Acin, “Extended local ergotropy”, Phys. Rev. Lett. 133,
150402 (2024).
[6] R. Castellano, R. Nery, K. Simonov, and D. Farina, “Parallel ergotropy: Maximum work extraction via
parallel local unitary operations”, Phys. Rev. A 111, 012212 (2025).

Bio

Donato Farina’s research interests are in quantum science and technology, in particular in the theory of open
quantum systems and quantum thermodynamics, but also quantum tomography, sensing and quantum
many-body physics.  
Donato Farina is currently an assistant professor (RTDa) at the University of Naples Federico II within the
NQSTI partnership. From 2021 to 2023, he worked as a postdoctoral researcher at ICFO in Barcelona, where
he was part of A. Acín’s Quantum Information Theory group. In 2021, he earned a Ph.D. in Nanoscience from
Scuola Normale Superiore of Pisa under the supervision of V. Giovannetti and M. Polini, defending the thesis
“Dissipative quantum systems: theoretical foundations and applications”. As an undergraduate student at
the University of Naples Federico II, he participated in a research internship at Fermilab (Chicago, USA) in
2015. In 2016, he completed another internship within a joint master’s thesis project at the Paris Diderot
University (Paris, France) working in experimental condensed matter physics.

This seminar is organized thank to the financial support of the project
PRIN 2022 - 2022XK5CPX (PE3) SoS-QuBa - "Solid State Quantum Batteries: Characterization and Optimization"
funded within the programme "PNRR Missione 4 - Componente 2 - Investimento 1.1 Fondo per il Programma Nazionale
di Ricerca e Progetti di Rilevante Interesse Nazionale (PRIN)", funded by the European Union - Next Generation EU.