Universal energy fluctuations in thermally isolated driven systems

Journal name:
Nature Physics
Year published:
Published online


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.

At a glance


  1. Two methods for changing the energy of a system.
    Figure 1: Two methods for changing the energy of a system.

    Schematic comparison between the usual thermal heating (traditional oven, top) and an energy increase due to non-adiabatic work (microwave oven, bottom). In the right column for each case we present a schematic picture of the resulting energy distribution.

  2. A particle in a driven chaotic cavity.
    Figure 2: A particle in a driven chaotic cavity.

    A single particle is bouncing in a deforming cavity of constant volume. The driving protocol consists in repeatedly deforming the cavity between the two shapes shown.


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Author information


  1. Department of Physics, Technion, Haifa 32000, Israel

    • Guy Bunin &
    • Yariv Kafri
  2. Department of Physics, Boston University, Boston, Massachusetts 02215, USA

    • Luca D’Alessio &
    • Anatoli Polkovnikov


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

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