Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus

In their work [Proc. Natl. Acad. Sci. USA 112 (2015) E5725], 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.Comment: 18 pages, no figures. Published versio

Statistical quantum operation

A generic unital positive operator-valued measure (POVM), which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize thermalization as a special case. The loss of information due to randomness generated by the operation is discussed by evaluating the entropy. Thermalization of the bipartite spin-1/2 system is discussed as an illustrative example.Comment: 10 pages, no figure

Stationary photon-atom entanglement and flow equation

Stationary photon-atom entanglement is discussed by applying the method of flow equation to the Jaynes-Cummings model. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method of flow equation. This method may offer a new strategy for quantum-state engineering.Comment: 21 pages, no figure

Conditional entropy and weak fluctuation correlation in nonequilibrium complex systems

The weak correlation between spatiotemporal fluctuations in nonequilibrium complex systems is shown to govern the fluctuation distribution, maximizing the conditional entropy associated with such fluctuations. The result is illustrated in diffusion phenomena observed in living cells. A generic feature of the weak correlation is briefly mentioned.Comment: 16 pages, no figures. For the proceedings of the 12th International Conference on Mathematical Modeling in Physical Sciences (August 28-31, 2023, Belgrade, Serbia

Deviation of the statistical fluctuation in heterogeneous anomalous diffusion

The exponent of anomalous diffusion of virus in cytoplasm of a living cell is experimentally known to fluctuate depending on localized areas of the cytoplasm, indicating heterogeneity of diffusion. In a recent paper (Itto, 2012), a maximum-entropy-principle approach has been developed in order to propose an Ansatz for the statistical distribution of such exponent fluctuations. Based on this approach, here the deviation of the statistical distribution of the fluctuations from the proposed one is studied from the viewpoint of Einstein's theory of fluctuations (of the thermodynamic quantities). This may present a step toward understanding the statistical property of the deviation. It is shown in a certain class of small deviations that the deviation obeys the multivariate Gaussian distribution.Comment: 17 pages, no figure