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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Chemical Continuous Time Random Walks.

Tomás Aquino1, Marco Dentz1

  • 1Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.

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|December 30, 2017
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Summary
This summary is machine-generated.

We introduce a generalized Gillespie algorithm to model chemical reactions with arbitrary delays, moving beyond the well-mixed assumption. This framework reveals new insights into non-Markovian kinetics and reaction dynamics under local nonequilibrium.

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Area of Science:

  • Biochemistry
  • Chemical Kinetics
  • Computational Chemistry

Background:

  • Kinetic Monte Carlo (KMC) methods, like the Gillespie algorithm, model chemical reactions as random walks.
  • Current KMC models assume exponentially distributed interreaction times, relying on the well-mixed system assumption.

Purpose of the Study:

  • To generalize KMC methods by incorporating arbitrary interreaction time distributions.
  • To account for the effects of incomplete mixing and stochastic reaction delays (extrinsic noise).

Main Methods:

  • Developed a framework for inhomogeneous continuous-time random walks in particle number space.
  • Derived a generalized chemical master equation and a modified Gillespie algorithm.
  • Analyzed modified chemical rate laws for various interreaction time distributions.

Main Results:

  • Introduced a generalized Gillespie algorithm accommodating arbitrary interreaction time distributions.
  • Connected finite-mean delay times to Michaelis-Menten-type kinetics.
  • Predicted time-nonlocal macroscopic reaction kinetics from broadly distributed delays.

Conclusions:

  • The generalized framework extends KMC modeling to systems with incomplete mixing and delays.
  • Non-Markovian kinetics arise from broadly distributed delays, exhibiting weak ergodicity breaking.
  • This approach provides a new perspective on reactions under local nonequilibrium conditions.