Scaling Law for Irreversible Entropy Production in Critical Systems.
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 ε0 of the initial state and the system size L. We find that, instead of depending on ε0 and L separately, this deviation exhibits a scaling behavior through a universal combination of ε0 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.
Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 37673, Korea.|National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.|Department of Natural Sciences, Quang Binh University, Dong Hoi, Quang Binh 510000, Vietnam.
Danh-Tai
DT
Hoang
Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 37673, Korea.|Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Technikerstraße 21a, Innsbruck 6020, Austria.|Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria.
B
B
Prasanna Venkatesh
Department of Physics, Korea University, Seoul 02841, Korea.
Seungju
S
Han
Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 37673, Korea.|Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk 37673, Korea.
Junghyo
J
Jo
Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 37673, Korea.|Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34051, Korea.|University of Science and Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea.|Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China.
Gentaro
G
Watanabe
Department of Physics, Korea University, Seoul 02841, Korea.
Mahn-Soo
MS
Choi