Supplemental Material
Quantum ratchet locally measured at site 𝜹.
For completeness we show the results when the quantum observer acts at site 𝜹 for the
quantum ratchet. Without the action of a local observer the particle current flows in
counter-clockwise direction. This steady-state current can be increased in this
direction by the action of the quantum observer at site 𝛿 , as shown in Fig. S1b.
Additionally, the local quantum observation can control the energy current as shown
in c.
Figure S1 | Influence of a quantum observation at site 𝜹 on the thermo-electric flows in
a quantum ratchet. Plot c shows the different energy currents in the top (𝒋𝒉𝐮𝐩 ) and bottom
(𝒋𝒉𝐝𝐨𝐰𝐧 ) branches while b shows the particle current in the upper branch, all as a function of
the coupling to the quantum observer (𝜸𝑫 ) and temperature difference (𝒌𝑩 𝜟𝑻).
Small changes in entropy production lead to emergent reversal of entropy flow.
Figure 5 illustrates that small changes in the entropy production rate (a) introduced by
the coupling to the quantum observers leads to a change in the direction of
thermodynamic flows (b). The difference between the changes of entropy production
and entropy flow as a function of the measurement strength drives the regimes of
transport. Quantum measurements can change the steady-state dynamics in ways
analogous to structures are dynamical states of matter that depend strongly and in
complicated ways to the amount of entropy production. In our model, the local action
of the quantum observer also adds irreversibility that breaks the existing symmetries
of the device, in turn, changing the direction of the heat flow and creates particle ringcurrents.
kB ∆ T (10− 4a.u.)
ΦH
P
b
Entropy Flow
γD /
p
✏0
a
10− 5
Entropy Production Rate
p
γD / ✏0
10− 4
kB ∆ T (10− 4a.u.)
Figure S2 | Entropy Production Rate and Entropy Flow to the hot bath for the ratchet
device in Fig. 3a. These quantities are defined in Eq. (2) in the main text. (a) The entropy
production rate increases with increasing temperature gradient 𝚫𝐓 and increasing observer
coupling. (b) Under the same conditions the entropy flow from the hot bath changes
differently in comparison to the entropy production rate, even changing signs. This illustrates
how minor changes in the entropy production rate can lead to abrupt changes in the
thermodynamics flows.