Universal energy fluctuations in thermally isolated driven systems

TL;DR

This paper investigates the universal properties of energy fluctuations in isolated driven systems undergoing cyclic processes, revealing a transition between different regimes and extending statistical physics understanding.

Contribution

It introduces the concept of universal energy distributions in non-adiabatically driven isolated systems and characterizes the transition between regimes.

Findings

Energy distribution becomes universal after many cyclic processes.

Identifies a second order-like transition between regimes.

Explicit calculations for interacting and non-interacting systems.

Abstract

When an isolated system is brought in contact with a heat bath its final energy is random and follows the Gibbs distribution -- 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 setup, which is especially relevant to recent experimental progress in cold atoms, ions traps, superconducting qubits and other systems. Here we show that when the non-adiabatic process comprises 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 performing explicit calculations for both interacting and non-interacting systems.