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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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This study explores the Jarzynski equality during phase transitions, revealing a universal scaling law for irreversibility deviations. This finding applies to both sudden and gradual quenches, offering insights into critical phenomena.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The Jarzynski equality relates equilibrium and non-equilibrium statistical mechanics.
  • Second-order phase transitions exhibit critical phenomena and spontaneous symmetry breaking.
  • Finite-sampling effects in initial equilibrium distributions are crucial for non-equilibrium studies.

Purpose of the Study:

  • To investigate the Jarzynski equality in a quenching process across the critical point of second-order phase transitions.
  • To analyze the impact of absolute irreversibility and finite-sampling on the Jarzynski equality.
  • To explore the scaling behavior of deviations from the Jarzynski equality.

Main Methods:

  • Utilizing the Ising model as a prototypical system for spontaneous symmetry breaking.
  • Introducing a tolerance parameter to account for finite-sampling of the initial equilibrium distribution.
  • Analyzing both sudden and finite-speed quenches within the Kibble-Zurek mechanism.

Main Results:

  • Deviations from the Jarzynski equality exhibit a universal scaling behavior dependent on a combined parameter of initial state and system size, not individually.
  • This scaling is inherited from the critical scaling laws of second-order phase transitions.
  • A similar scaling law was observed for finite-speed quenches.

Conclusions:

  • The study reveals a universal scaling law governing deviations from the Jarzynski equality in critical phenomena.
  • Finite-sampling and irreversibility effects are intrinsically linked and scale universally.
  • The findings provide a deeper understanding of non-equilibrium statistical mechanics near critical points.