Converting phonon heat into electrical power via nonlocal virtual asymmetric resonance! So the heat current is converted to a charge current. you get electron phase accumulation then as energy increase.
Carnot efficiency is the maximum theoretical efficiency any heat engine can achieve operating between two temperatures, given by \(\eta_{C} = 1 - T_{c}/T_{h}\) (\(T_{c}\)=cold, \(T_{h}\)=hot in Kelvin). It represents a perfectly reversible cycle where no energy is wasted, setting the benchmark limit for real-world engines, which typically only reach about 70% of this maximum
Charge is not conserved. Electrons go one direction and holes go the opposite direction. The left-right symmetry has to be broken to create a circulating current. The heat is perpendicular to the current so the heat can be separated between the hole and electron current....heat can be extracted or current extract.
http://webs.ftmc.uam.es/rafael.sanchez/
Universidad Autónoma de Madrid
https://orcid.org/0000-0002-8810-8811
You Extract the Hole!! necessary symmetry breaking energy transfer
Making the virtual real: Measurement-powered tunneling engines
Physical Review B
2026-03-09
|
Journal article
Contributors:
Rafael Sánchez;
Alok Nath Singh;
Andrew N. Jordan;
Bibek Bhandari
https://scholar.google.com/citations?user=Ngha00cAAAAJ&hl=en
you 
https://arxiv.org/pdf/2503.10064
recognizing that the measurement process itself plays an active role in localizing the particle in the classically forbidden virtual state...the measurement process not only extracts information but also injects energy into the system, effectively enabling the particle to transiently occupy the virtual state. ... the virtual state is indeed populated during tunneling. If it were not so, there would be no interaction between the electrons in the TQD and the QPC, and ρCC wouldn’t be affected. Note that the energy needed to populate C is provided by the measurement device, since the measurement operator, ˆLγ , does not commute with ˆHTQD....measurements can fundamentally alter the presence of an electron in the virtual state, offering a deeper insight into the role of observation in understanding the virtual states.
we investigate the interplay between virtual transitions and measurement back-action, proposing an experiment based on a triple quantum dot system under the continuous measurement of a highly-detuned central dot.
The quantum dot is switching the gates...
https://arxiv.org/html/2510.22394
Making the Virtual Real: Measurement-Powered Tunneling Engines
https://arxiv.org/pdf/2504.09121
https://arxiv.org/pdf/2508.03659
https://arxiv.org/pdf/2510.22394
When the central dot is strongly detuned from the two external ones, hopping between left and right dots (fed by two electronic reservoirs) occurs via virtual tunneling transitions [31–
39].
By continuously monitoring the central quantum dot, virtual tunneling events are converted into real occupations, enabling two key functionalities: (i) thermodynamic operations, including power generation, refrigeration, and hybrid energy conversion, and (ii) quantum state purification, where noise from the detector stabilizes the system into a dark state.
https://par.nsf.gov/servlets/purl/10603968
the trajectories exhibit quantum jumps between the dynamically stabilized regions of local oscillations around the eigenstates. Since these transitions are otherwise forbidden, this is a measurement-induced tunneling effect and is closely related to that recently predicted for tunneling through a triple quantum dot (Singh et al., 2025). The short-time behavior clearly shows the localized oscillations being perturbed by the measurement.
https://iopscience.iop.org/article/10.1088/2058-9565/ae1e27/pdf#164
Moreover, there is the possibility of several non-commuting operators of the system to couple to multiple baths, which can lead to significantly increased system-bath entanglement [246]. The exploration of non-commuting coupling operators is still in its infancy, and bridges to non-Abelian thermal states (NATSs) discussed in section 17
Jakub Garwoła and Dvira Segal, "Open quantum systems with noncommuting coupling operators: An analytic approach", Physical Review B 110 17, 174304 (2024).
a qubit concurrently coupled to both decohering and dissipative baths.
Our approach, which accommodates strong system-bath couplings,
generalizes the recently developed reaction-coordinate polaron transform
method [N. Anto-Sztrikacs et al., PRX Quantum 4, 020307 (2023)]
to handle couplings to baths via noncommuting system operators. Our
approach creates an effective Hamiltonian that reveals the cooperative
effect of the baths on the system
h the phonon bath acting as the heat source.
https://arxiv.org/pdf/2504.09121
In these setups the electron-hole symmetry is broken by the kinetic phase accumulated between the junctions connecting the ring to the differ-
ent terminals [248, 249], with broken time-reversal symmetry introducing the mirror asymmetry (via the non
reciprocity of the transmission probabilities Tij (B)̸ =Tji(B)) needed for the thermocouple effect, even if the geometric configuration of the system is symmetric and energy-independent [164]. To see this, consider a symmetric ring with all three terminals equally separated by one third of the ring perimeter, so we have T⟳(ϕ) = T12(Φ) = T23(Φ) = T31(Φ).
nonlocal thermoelectrics mediated by interactions
Phonon assisted tunneling between two quantum dots provides the energy, ℏωp ≈ εR − εL ≫ λ to
overcome an energy gap, where λ is the interdot coupling, and Γ are the tunneling rates for coupling with the reservoirs. The splitting of the quantum dot levels introduce all the required broken symmetries naturally.
the two transitions in the source
dot, g, perform the detection (of the charge in s), feed-
back (the charge in g affecting the tunneling rates in the
conductor) and information erasure (restoring the ini-
tial state) mechanisms of an autonomous Maxwell de-
mon. This is most clearly evidenced in the equivalent
case where the nonlocal thermoelectric response is due to
coupling to a colder source [118], where the sequence is
reversed: (n1, n2) = (0, 0) → (0, 1) → (1, 1) → (1, 0) →
(0, 0). The cold dot, g, is occupied until an electron enters
s, when it absorbs the energy U to overcome the electro-
chemical potential μg and tunnel out (detection). This
changes the rates in the system (backaction) allowing the
electron to tunnel out and restores the initial state (re-
set). In this case, U is transferred from s to g, increasing
the entropy of the gate.
Differently from what one expects from a Maxwell de-
mon though, a three terminal configuration cannot re-
duce the entropy of the conductor by, e.g., generating
power, without changing its energy: a finite JH̸ = 0
is necessarily exchanged via the electron-electron inter-
action in the quantum dots, see Eq. (16). References
[68] and [306] are then rather interpreted as autonomous
information-enabled (demonic) heat engines [122]
https://arxiv.org/pdf/2408.01865
The two nontrivial elements of our study are
the coupling of the system to the baths beyond the
weak coupling limit and through noncommuting system
operators. The first challenge in solving the dynamics of
the system described by Eq. (1) arises from its potentially
strong coupling to the environments, which precludes
a low-order perturbative treatment.
the construction of genuine quantum effects in quantum
thermal machines, emerging due to the combination
of noncommutativity, strong system-bath coupling, and
nonequilibrium conditions.
https://iopscience.iop.org/article/10.1088/2058-9565/ae1e27/pdf
Noncommuting charges
charges’ noncommutation can change entanglement entropy and thermodynamic-entropy
production. As a quantum many-body system thermalizes internally, its constituent particles entangle.
To pinpoint how charges’ noncommutation affects entanglement, researchers built two models [296].
Each is a one-dimensional chain of two-qubit sites. The models parallel each other, such as by having
the same number of charges, which have the same eigenvalues. However, one model’s charges commute,
and the other model’s do not. The noncommuting-charge model achieved a greater average bipartite
entanglement entropy than its counterpart. However, charges’ noncommutation can decrease average
thermodynamic entropy production, which quantifies irreversibility
https://arxiv.org/pdf/2504.09121
the nanostructure acts as a filter to break electron-hole symmetry....this dependence also breaks
inversion (left-right) symmetry, i.e., TLH (E)̸ = cTRH (E),
with c a positive number. ...symmetry breaking must
be a property of the conductor,
the three-terminal scat-
tering matrix (composed of the barrier and the tip) suf-
ficient to break the electron-hole symmetry [242]. Mean-
while, the inversion symmetry is broken geometrically by
the position of the tip with respect to the barrier.
When quantum interference is the only responsible of the electron-hole energy
breaking, the nonlocal thermoelectric effect is indeed af-
fected by dephasing
therefore Tp − T
breaks the detail balance of the phonon-assisted tunnel-
ing transition. This mechanism enables the direct elec-
tric current, which can be controlled by gating the quan-
tum dot levels
nonlocal thermoelectric converters have been pro-
posed based on this effect in a variety of setups, including
molecules [125, 142, 167, 168], quantum dots [167, 313]
or suspended wires [145, 168, 239, 314]. In multiterminal
(two electronic, two phononic) configurations, interest-
ing connections between phonon drag and pumping have
been suggested [188].
introducing virtual probes to the problem, where electrons propagating
along the conductor can be absorbed and reinjected,
electrons in the two dots where the interacting state (1, 1) is only virtually occupied [137, 138, 299] become important. In this regime,
the energy filtering introduced by the discreteness of the
quantum dot levels becomes broader, which can help to
improve the amount of generated power [137].
Rafael Sánchez - Quantum thermoelectrics
Electrons in a conductor react not only to voltage but also to temperature gradients. In their motion, they carry electric charge as well as energy. This makes it possible to think of devices that are absorb excess heat from their environment and convert it into useful power. This can be done in three terminal devices: Two terminals support the charge current with the third one serving as the heat source, enabling the separation of charge and heat flows.
Mesoscopic (nanoscale) systems are good candidates for this, because of their high degree of tunability and rich variety of different effects that allow for the mechanism of heat to power conversion:
Coulomb interactions [1], resonant tunneling [2], entanglement [3], quantum interference, or the absence of thermalization [4].
Nonlocal heat engines with hybrid quantum dot systems by Dr. Rafael Sanchez
potential and the temperature of this of this probe terminals are
floating so it's like a thermometer so so they they evolve until this this uh
this condition is fulfilled uh so this is yeah this is what a
thermometer does so for example to see if in Us in in the simplest case where
where the this this scattering Matrix is transparent so all of all every electron
from two goes into the probe and then goes back to the system uh and also from
the from the left so so there is no scatter
the only consumed resource being the continuous measurement. Compared to classical analogues, the
generated current is enhanced while noise is reduced
