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The Non-equilibrium Nature of Active Motion

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Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues

Abstract

In this contribution chapter, the non-equilibrium nature of active motion is explored in the framework of the Generalized Langevin Equation. The persistence effects that distinguish active motion, observed in a variety of biological organisms and man-made colloidal particles, from the passive one, are put in correspondence with the memory function that characterizes the retarded dissipative effects in the equation. The non-equilibrium aspects of this approach rely on the relaxation of the fluctuation-dissipation relation, that couples the memory function with the autocorrelation function of the fluctuating force in order to describe the equilibrium. In the case of freely diffusing active particles, the Fokker-Planck equation is derived and an effective temperature can be identified if the total overlap between the deterministic solutions of the Generalized Langevin Equation at two times, weighted by the noise correlation function, exists and is finite. Active motion confined by the harmonic, external potential is analyzed on the same framework leading to analogous conclusions.

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Acknowledgements

The author kindly acknowledges the support from grant UNAM-DGAPA-PAPIIT-IN114717.

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Authors and Affiliations

  1. Instituto de Fisica, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, CD.MX., Mexico City, Mexico

    Francisco J. Sevilla

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  1. Francisco J. Sevilla
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Correspondence to Francisco J. Sevilla .

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Editors and Affiliations

  1. Universidad Autónoma de la Ciudad de México (UACM), Mexico City, Mexico

    Luis Olivares-Quiroz

  2. Human Systems Biology Laboratory, Instituto Nacional de Medicina Genómica (INMEGEN), México City, Mexico

    Osbaldo Resendis-Antonio

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Sevilla, F.J. (2018). The Non-equilibrium Nature of Active Motion. In: Olivares-Quiroz, L., Resendis-Antonio, O. (eds) Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues. Springer, Cham. https://doi.org/10.1007/978-3-319-73975-5_4

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