Most of our knowledge on heat machines, molecular machines and chemical networks is based on the assumption that at thermal equilibrium systems keep what is called local detailed balance. Local detailed balance means that, at thermal equilibrium, the rate between any pair transitions is perfectly balanced by the rate of the opposite transition.

Any deviation from this balance requires the system to be out of equilibrium, resulting in the flow of currents in mesoscopic junctions, the transformation of energy in solar cells, or the realization of several biological functions in living systems. Breaking detailed balance is thus an essential thermodynamic resource with several applications.

Non-reciprocal systems have the peculiarity of breaking detailed balance even at equilibrium. This has resulted in many surprising effects: persistent heat currents in thermal equilibrium, violations of the Kirchhoﬀ law, photon thermal hall eﬀect and giant magnetoresistance for the heat ﬂux. We recently found that non-reciprocal materials are needed in order to build a heat engine based on Casimir forces. What other exciting effects can be produced by non-reciprocal systems?

We are investigating this question by building a thermodynamic framework to study non-reciprocal systems and discover other peculiar thermodynamic effects. Moreover, by examining the systems that do not comply with the common assumption of local detailed balance, we are exploring uncharted territories and sharpening the theory of thermodynamics.

**Some of the questions that we are studying are:**

- What are the limitations that thermodynamics impose on these systems?
- What is the basic thermodynamic behavior of non-reciprocal systems?

**Some of our papers:**

*Casimir heat engine using non-reciprocal materials*

Near field propulsion forces from non-reciprocal media

Gelbwaser-Klimovsky, D., Graham, N., Kardar, M., & Krüger, M., *Physical Review Letters* 126.17 (2021): 170401. (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.170401)

https://arxiv.org/abs/2012.12768

**Other groups papers: **

*Persistent heat currents in thermal equilibrium*

Persistent directional current at equilibrium in non-reciprocal many-body near field electromagnetic heat transfer

Zhu, L., and Fan S. *Physical review letters* 117.13 (2016): 134303. (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.134303)

https://arxiv.org/abs/1602.08454

Excellent reviews on non-reciprocity:

Electromagnetic non-reciprocity

Caloz, C., Alu, A., Tretyakov, S., Sounas, D., Achouri, K., & Deck-Léger, Z. L. (2018). . *Physical Review Applied*, *10*(4), 047001.(https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.10.047001)

https://arxiv.org/abs/1804.00235

Tutorial on electromagnetic non-reciprocity and its origins

Asadchy, V. S., Mirmoosa, M. S., Díaz-Rubio, A., Fan, S., & Tretyakov, S. A. (2020). *Proceedings of the IEEE*, *108*(10), 1684-1727.

(https://ieeexplore.ieee.org/document/9163137)

https://arxiv.org/abs/2001.04848

Non-equilibrium devices such as thermoelectric devices, solar cells, and heat machines exploit energy/particle currents that flow through a system coupled to multiple baths. Although the fluxes increase as the coupling strengthens in the weak coupling regime, why they decrease to zero for large coupling values remains unknown. This turnover effect has been predicted in several systems such as photosynthetic complexes, thermoelectric devices and chemical networks, without a single counterexample, resulting in a constrained performance due to the limited currents. We also found that this effect limits the performance of heat machines.

These are

EXPLORE

**The “Turnover Effect” In Heat Engines**

Strongly Coupled Quantum Heat Machines

Gelbwaser-Klimovsky, D. & Aspuru-Guzik, A. J. Phys. Chem. Lett. 6, 3477–3482 (2015)

EXPLORE

**The “Turnover Effect” In Heat Engines**

Strongly Coupled Quantum Heat Machines

Gelbwaser-Klimovsky, D. & Aspuru-Guzik, A. J. Phys. Chem. Lett. 6, 3477–3482 (2015)

The concept of temperature is a central part of equilibrium thermodynamics and statistical mechanics: it is related to several thermodynamics’ laws, it is the key parameter of the equilibrium distribution, and even sets eﬃciency limitations to work extraction (Carnot bound). No wonder why so many have tried to extend the notion of temperatures to the realm of non-equilibrium systems.

This is achieved by deﬁning an eﬀective temperature, which is generally related to a violation of the ﬂuctuation-dissipation theorem or the use of colored noise. The introduction of an eﬀective temperature has helped reveal the nature of molecular motors in red-blood cell membranes, set bounds to the performance of active Brownian engines, study glasses, and more. Though in some cases the use of an eﬀective temperature provides a good phenomenological description, the models used tend to either use unphysical assumptions such as negative friction or lack a microscopic model that could explain the physical nature of the disequilibrium and its thermodynamic repercussions.

We use the notion of effective temperatures for discovering the limitations that thermodynamics imposes on non-equilibrium systems. To achieve this, we are taking a unique approach and defining effective temperatures from a microscopic physical model. We have already shown that simple properties of these effective temperatures determine the thermodynamic capabilities of a non-equilibrium system. What else can the effective temperature tell us about non-equilibrium systems? For determining this we are studying the concept of effective temperatures in different systems.

**Some of the questions we are studying are:**

- What are the limitations that thermodynamics imposes on non-equilibrium systems?
- What could the effective temperature teach us about the thermodynamics properties of a system?

**Our papers**

*Effective temperatures in quantum systems:*

Non-equilibrium quantum heat machines

Alicki, R., and Gelbwaser-Klimovsky, D. *New Journal of Physics* 17.11 (2015): 115012

(https://iopscience.iop.org/article/10.1088/1367-2630/17/11/115012)

https://arxiv.org/abs/1507.01660

**Other groups papers**

* *

*A good review about the effective temperature*

he effective temperature

Cugliandolo, Leticia F. *Journal of Physics A: Mathematical and Theoretical* 44.48 (2011): 483001. (https://iopscience.iop.org/article/10.1088/1751-8113/44/48/483001)

https://arxiv.org/abs/1104.4901

*An example of the application of effective temperature to study red-blood-cell*

Effective temperature of red-blood-cell membrane fluctuations

Ben-Isaac, E., Park, Y., Popescu, G., Brown, F. L., Gov, N. S., & Shokef, Y. (2011) . *Physical review letters*, *106*(23), 238103. (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.238103)

https://arxiv.org/abs/1102.4508

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