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Statistical fluctuations in chiral symmetry breaking favor populations, with favoring probability decreasing exponentially with initial enantiomeric deficiency. Initial enantiomeric excess is not solely responsible for the final configuration in finite systems.

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Area of Science:

  • Chemistry
  • Physics
  • Biochemistry

Background:

  • Chiral symmetry breaking is a fundamental process in nature.
  • Statistical fluctuations play a crucial role in natural chiral processes.
  • Understanding the influence of initial conditions on chiral symmetry breaking is essential.

Purpose of the Study:

  • To investigate the probabilistic favoring of populations in chiral symmetry breaking under statistical fluctuations.
  • To develop a quantitative understanding of how enantiomeric excess or deficiency affects chiral symmetry breaking.
  • To explore the role of population size and statistical fluctuation amplitude.

Main Methods:

  • Stochastic methods were employed to model chiral symmetry breaking.
  • The autocatalytic Frank model was utilized to study these processes.
  • Quantitative enantiomeric difference and statistical fluctuation amplitude were considered.

Main Results:

  • A law was derived showing favoring probability decreases exponentially with initial enantiomeric deficiency [P(EE) = 1/(eαEE + 1)].
  • Chiral symmetry breaking equally favors populations without enantiomeric excess (P(0) = 1/2) under stochastic conditions.
  • Deterministic methods show a strict preference for initial enantiomeric excess.

Conclusions:

  • Initial enantiomeric excess is not the sole determinant of final configurations in finite autocatalytic systems.
  • Stochastic fluctuations significantly influence the outcome of chiral symmetry breaking.
  • The size of the population and fluctuation amplitude are inversely related to favoring probability.