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Powerful Ordered
Collective Heat Engine
Fernando Silva
Instituto de Física da Universidade de São Paulo
Engines with single units setup
One single quantum 
dot with two states in
contact with several
thermal baths
however…..
A single Brownian particle 
under a harmonic potential 
in contact with reservoirs
Engine in a complex environment
Extracted from:
Leduc C, et al.,
Proc Natl Acad Sci U S A. 2012 
Apr 17;109(16):6100-5. 
Extracted from:
L.da Silva Souza, et al.,
Phys. Rev. E 106, 014143, 2022
Our proposed model
Stochastic thermodynamics on NESS
A non-equilibrium phase diagram
Power and efficiency for q =3 
Power and efficiency for q =2 
The same for q=2
Role of 𝝰 in q =3 (Strength of opposite spin interaction)
The role of the number of engines (spins)
For finite N we used a Gillespie Algorithm
There are more!
● An analytical approximation using an effective ordered phase
● Analysis through the Onsager coefficients in the near-equilibrium approximation
OPEN ACCESS!!
THANK YOU

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