Time evolution of entropy associated with diffusivity fluctuations: Diffusing diffusivity approach
arXiv:1901.05291 · doi:10.1140/epjb/e2019-100054-9
Abstract
It has experimentally been found by Lampo et al. [Biophys. J. 112, 532 (2017)] that, for two different types of cell, the distribution of the diffusivities of RNA-protein particles over cytoplasm obeys an exponential law. Then, an interesting issue has been pointed out: this exponential distribution is the maximal entropy distribution. Here, time evolution of entropy associated with local fluctuations of the diffusivity is studied. The entropy rate under the diffusing diffusivity equation, which admits the exponential fluctuation as its stationary solution, is shown to be positive. The present result is expected to be useful for studying the dynamics of diffusivity fluctuations. Furthermore, the distribution of time being required for characteristic displacement of the RNA-protein particle is found to decay as a power law. A comment is also made on a formal analogy with the thermodynamic relation concerning temperature.
17 pages, no figures. Published version
References in corpus (7)
- Anomalous transport in the crowded world of biological cells
- "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
- Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
- Superstatistical distributions from a maximum entropy principle
- Heterogeneous anomalous diffusion in view of superstatistics
- Deviation of the statistical fluctuation in heterogeneous anomalous diffusion
- Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus
Cited by in corpus (7)
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- Fluctuating diffusivity of RNA-protein particles: Analogy with thermodynamics
- Conditional entropic approach to nonequilibrium complex systems with weak fluctuation correlation
- Weak correlation between fluctuations in protein diffusion inside bacteria
- Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity
- Analog of the Carnot engine for fluctuating diffusivity in living cells
- On the thermodynamic analogy of intracellular diffusivity fluctuations