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Universal energy fluctuations in thermally isolated driven systems


When an isolated system is brought in contact with a heat bath, its final energy is random and follows the Gibbs distribution—this finding is a cornerstone of statistical physics. The system’s energy can also be changed by performing non-adiabatic work using a cyclic process. Almost nothing is known about the resulting energy distribution in this set-up, which is in particular relevant to recent experimental progress in cold atoms, ion traps, superconducting qubits and other systems. Here we show that when the non-adiabatic process consists of many repeated cyclic processes, the resulting energy distribution is universal and different from the Gibbs ensemble. We predict the existence of two qualitatively different regimes with a continuous second-order-like transition between them. We illustrate our approach by performing explicit calculations for both interacting and non-interacting systems.

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Figure 1: Two methods for changing the energy of a system.
Figure 2: A particle in a driven chaotic cavity.


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The authors would like to thank G. Ortiz for the comment related to a cumulant expansion of the Jarzynski equality which plays an important role in the proof. The authors also acknowledge the support of the NSF DMR-0907039 (A.P.), AFOSR FA9550-10-1-0110 (L.D. and A.P.), Sloan Foundation (A.P.). Y.K. thanks the Boston University visitors program for its hospitality.

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G.B, L.D, Y.K and A.P contributed equally to this project.

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Correspondence to Anatoli Polkovnikov.

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The authors declare no competing financial interests.

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Bunin, G., D’Alessio, L., Kafri, Y. et al. Universal energy fluctuations in thermally isolated driven systems. Nature Phys 7, 913–917 (2011).

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