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Mean back relaxation for position and densities.

Gabriel Knotz1, Matthias Krüger1

  • 1Institute for Theoretical Physics, <a href="https://ror.org/01y9bpm73">University of Göttingen</a>, 37077 Göttingen, Germany.

Physical Review. E
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Summary
This summary is machine-generated.

Mean back relaxation (MBR) analyzes particle trajectories. Its deviation from 1/2 signals broken time-reversal symmetry and detailed balance in confined or bulk systems.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Physical Chemistry

Background:

  • Correlation functions are essential for analyzing particle trajectory data.
  • Mean back relaxation (MBR) is a recent metric correlating particle positions across three time points.
  • MBR's deviation from 1/2 indicates broken time-reversal symmetry in confined systems.

Purpose of the Study:

  • Extend the analysis of mean back relaxation (MBR).
  • Provide a general expression for MBR using path integral methods.
  • Demonstrate MBR's applicability to other stochastic observables.

Main Methods:

  • Path integral formulation to derive MBR expression.
  • Analysis of MBR in relation to multipoint density correlations.
  • Investigation of MBR with a cutoff length for trajectory data.

Main Results:

  • A general MBR expression derived in terms of multipoint density correlations.
  • For Gaussian systems, MBR is related to mean-squared displacement.
  • MBR deviation from 1/2 serves as a marker for broken detailed balance.

Conclusions:

  • MBR is a versatile tool for detecting broken time-reversal symmetry and detailed balance.
  • The study provides theoretical underpinnings and broadens MBR's application scope.
  • MBR analysis is effective for both confined and bulk stochastic systems.