### Abstract

We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ϵ_{0} of the initial state and the system size L. We find that, instead of depending on ϵ_{0} and L separately, this deviation exhibits a scaling behavior through a universal combination of ϵ_{0} and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism.

Original language | English |
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Article number | 27603 |

Journal | Scientific Reports |

Volume | 6 |

DOIs | |

Publication status | Published - 2016 Jun 9 |

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### ASJC Scopus subject areas

- General

### Cite this

*Scientific Reports*,

*6*, [27603]. https://doi.org/10.1038/srep27603