[en] Highlights: • A theory is developed for a generalized fractional kinetics in view of superstatistics. • The present theory explicitly takes into account the existence of a large time-scale separation in the infection pathway. • The present theory implies a scaling nature of the motion of the virus. - Abstract: It is experimentally known that virus exhibits stochastic motion in cytoplasm of a living cell in the free form as well as the form being contained in the endosome and the exponent of anomalous diffusion of the virus fluctuates depending on localized areas of the cytoplasm. Here, a theory is developed for establishing a generalized fractional kinetics for the infection pathway of the virus in the cytoplasm in view of superstatistics, which offers a general framework for describing nonequilibrium complex systems with two largely separated time scales. In the present theory, the existence of a large time-scale separation in the infection pathway is explicitly taken into account. A comment is also made on scaling nature of the motion of the virus that is suggested by the theory

[en] The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

[en] 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. Graphical abstract:

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[en] Highlights: • Diffusion-exponent fluctuations of virus capsid in a cell nucleus are studied. • Local areas of interchromatin corrals are regarded as cubic blocks. • Largeness of the number of blocks is examined. • The Gaussian distribution of the fluctuations is derived by the maximum entropy principle. • Difference of the fluctuation distribution from the Gaussian distribution is quantified. - Abstract: In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.