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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Topological phases in discrete stochastic systems.

Jaime Agudo-Canalejo1, Evelyn Tang2

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This summary is machine-generated.

Topological invariants offer robust protection in complex systems. This review explores their application in non-equilibrium and stochastic biological systems, revealing principles for synthetic engineering and robust function.

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Area of Science:

  • Physics
  • Complex Systems
  • Biophysics

Background:

  • Topological invariants characterize systems robustly, insensitive to local disorder.
  • They support boundary states and global cycles, extensively studied in quantum and mechanical systems.
  • Existing frameworks primarily address equilibrium, ordered crystalline lattices.

Purpose of the Study:

  • Review recent developments in topological states within discrete stochastic models.
  • Explore initial progress in identifying topological signatures in molecular and ecological systems.
  • Discuss novel theoretical properties and analytical tools for non-equilibrium topological systems.

Main Methods:

  • Review of discrete stochastic models in 1D and 2D systems.
  • Analysis of theoretical advancements in non-Hermitian systems and edge states.
  • Exploration of new analytical tools for topological property detection.

Main Results:

  • Topological states are being identified in non-equilibrium, stochastic systems.
  • Progress in detecting topological signatures in molecular and ecological contexts.
  • Novel theoretical insights into non-Hermiticity and edge states in topological systems.

Conclusions:

  • Topological principles are applicable to non-equilibrium and stochastic systems, including biological ones.
  • These findings offer pathways for targeted dynamics in synthetic systems and reconfigurable materials.
  • Emerging developments illuminate fundamental principles for robust biological function via topological protection.