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Far-from-equilibrium complex landscapes.

Laura Guislain1, Eric Bertin1

  • 1Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France.

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Summary
This summary is machine-generated.

We generalize complex landscape theory for systems far from equilibrium, revealing hidden collective time-dependent states like oscillations. A new configurational entropy measure quantifies these emergent oscillating states in complex spin models.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Non-equilibrium Physics

Background:

  • Complex dynamics in systems like glasses and biological evolution are often modeled using complex landscapes with numerous collective states.
  • Understanding these landscapes far from equilibrium, where states can be time-dependent, remains a challenge.

Purpose of the Study:

  • To generalize the complex landscape picture for systems operating far from thermodynamic equilibrium.
  • To identify methods for revealing hidden time-dependent collective behaviors, such as spontaneous oscillations, in disordered systems.

Main Methods:

  • Utilized a stochastic spin model featuring nonreciprocal and heterogeneous interactions.
  • Introduced and analyzed the density of entropy production rate as a key observable.
  • Developed a configurational entropy to count oscillating collective states.

Main Results:

  • Demonstrated that collective states can become time-dependent, exhibiting spontaneous oscillations even in the presence of disorder.
  • Identified the density of entropy production rate as an effective observable to detect this hidden collective time dependence.
  • Found that the number of oscillating collective states grows exponentially with system size, quantifiable by the configurational entropy.

Conclusions:

  • The complex landscape concept can be extended to far-from-equilibrium systems with time-dependent collective states.
  • Spontaneous collective oscillations are a feature of such systems, detectable through specific observables.
  • Configurational entropy provides a measure of the complexity and richness of emergent dynamics in these non-equilibrium systems.