Table of contents

Preface

The present volume contains 10 contributed papers presented at the meeting on "Nonequilibrium thermodynamics and statistical physics: From rational modeling to its applications" held during March 16 – 17, 2017 in Hakata, Japan. Each submitted contributed paper was peer-reviewed by at least one referee.

The meeting was dedicated to 66th birthday of Prof. Masaru Sugiyama in Nagoya Institute of Technology. The aim of this meeting is to provide the related researchers in the fields of nonequilibrium thermodynamics and statistical physics with an opportunity to get together and to exchange their recent results. Main topics of the meeting are the following:

• Rational extended thermodynamics

• Nonequilibrium statistical physics

• Kinetic theory of rarefied gases

• Nonlinear wave propagation

• Computational fluid dynamics

• Numerical simulation on material science

Valuable discussions from the viewpoints of theoretical physics, chemical physics and applied mathematics were also made after the talks.

This international meeting attracted 15 participants from 3 countries, namely, Japan, Italy and China. 12 oral contributions were presented at the meeting.

We would like to thank all participants for their essential contributions to the success of the meeting. We are also grateful to the reviewers for their careful reading and prompt response. The meeting was partially supported by JSPS KAKENHI Grant Numbers JP16K17555 (S. T.) JP15K21452 (T.A.) and by National Institute of Technology, Kitakyushu College, Japan.

Editors: Shigeru Taniguchi and Takashi Arima

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

A brief review of two recent topics on the Lindblad equation is presented. One is concerned with time evolution of the quantum Rényi entropy under the equation. The lower bound of the entropy rate is derived in a compact form. The other is about the concept of weak invariants, which generalize the Lewis-Riesenfeld invariant and are defined in such a way that they are not constant but their expectation values remain invariant in time. The Lindbladian operator describing the time-dependent damped quantum oscillator is identified, and the corresponding weak invariant is explicitly constructed as an example.

In the framework of extended thermodynamics, we present three models of a dense polyatomic gases with 6 independent fields. The three models, respectively, represent the relaxation process due to the different molecular energy exchange among the translational, rotational and vibrational energies of a molecule. The characteristic velocities, the local exceptionality and the Maxwellian iteration are also studied. As an example, we study the six-field models of a van der Waals fluid.

We describe qualitatively some 2D stationary problems for metal electrons in the presence of a temperature gradient and a magnetic field. To this aim we refer to a linearized Extended Thermodynamics model that allows a semianalytical construction of the solutions. The results are in agreement with the thermomagnetic effects already known in the literature.

The deviation of the statistical distribution of the diffusion-exponent fluctuations from a Poisson-like distribution is discussed for virus in cytoplasm of a living cell. The deviation is shown to obey the multivariate Gaussian distribution for a class of small deviations. A brief discussion is also made about the behavior of such a deviation from a geometric viewpoint.

We propose a possible generalization of the BGK collisional term in the relativistic kinetic theory and we compare our model with previous ones. The present model has the advantage in that it satisfies the conservation of particle number, energy-momentum and the H-theorem in the Eckart frame without constraints on particular local equilibrium state. In the last part of the paper we extend the model to include also the polyatomic gas.

In the present paper, we establish a theoretical formalism to study the protein-protein association rate in the framework of diffusion-limited theory. To account for the crowding effect due to the presence of polymer, we particularly take into account the deviation of rotational diffusion of proteins from the Stokes-Einstein-Debye relation. Based on fluid mechanics and depletion theory, a new scaling relation for the retardation factor of the rotational diffusion was proposed. Besides, the crowding-induced interaction energy between the proteins has been also properly introduced into the association rate theory. We apply our theory to calculate the association rate constant of proteins β-lactamase and β-lactamase inhibitor protein in poly(ethylene glycol) solutions. Particular attention is paid to the dependence of the association rate constant on the polymer concentration and polymer molecular weight. The deviation from the simple relation based on Stokes-Einstein approximation is well addressed. We find that our theoretical results show good agreements with the experimental data in the whole concentration region, which demonstrates the validity of our theory.

A case study was conducted for simulated processes of magnetosphere-ionosphere (M-I) coupling process using a magnetohydrodynamic (MHD) simulation code developed by Tanaka (2010). We combined the MHD simulation and solar wind parameters derived from the ACE satellite, and compared the ionospheric E × B plasma drift obtained from the global MHD simulation and that obtained from the SuperDARN HF Radar Network. The simulated plasma drift was not always reproducible under a southward interplanetary magnetic field (IMF) condition. We believe that the M-I boundary conditions in the global MHD simulation includes insufficient factors for the M-I coupling process.

Steady flow of a polyatomic gas is studied by the extended thermodynamic theory with six independent fields (ET₆). It is shown that the ET₆ theory can describe the effects on a flow due to the relaxation process of the internal motion such as molecular rotation and vibration, which can not be predicted by the Euler perfect fluid theory. And thereby characteristic features of the ET₆ theory itself can be elucidated.

The shock wave structure in rarefied polyatomic gases is analyzed based on extended thermodynamics (ET). In particular, the case with large relaxation time for the dynamic pressure, which corresponds to large bulk viscosity, is considered by adopting the simplest version of extended thermodynamics with only 6 independent fields (ET₆); the mass density, the velocity, the temperature and the dynamic pressure. Recently, the validity of the theoretical predictions by ET was confirmed by the numerical analysis based on the kinetic theory in [S Kosuge and K Aoki: Phys. Rev. Fluids, Vol. 3, 023401 (2018)]. It was shown that numerical results using the polyatomic version of ellipsoidal statistical model agree with the theoretical predictions by ET for small or moderately large Mach numbers. In the present paper, first, we compare the theoretical predictions by ET₆ with the ones by kinetic theory for large Mach number under the same assumptions, that is, the gas is polytropic and the bulk viscosity is proportional to the temperature. Second, the shock wave structure for large Mach number in a non-polytropic gas is analyzed with the particular interest in the effect of the temperature dependence of specific heat and the bulk viscosity on the shock wave structure. Through the analysis of the case of a rarefied carbon dioxide (CO₂) gas, it is shown that these temperature dependences play important roles in the precise analysis of the structure for strong shock waves.

Effects of smoothing of point force used in the two-way coupling simulation of particle-laden turbulent flow are examined for one dimensional simple model and for the Eulerian-Lagrangian simulations of polymers in turbulence. We show that the regularization by using Gaussian function yields preferable behavior in evaluating the smoothed point force compared to the conventional methods used in the previous studies. An efficient computational scheme to use the approximated Gaussian function is newly developed for the two-way coupling simulation in which the turbulent field is solved by using the spectral method. This scheme is applied to the Eulerian-Lagrangian simulations for examining polymer-turbulence interactions.