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Entropy is a fundamental concept in physics. It appears in thermodynamics, statistical mechanics, information theory, computation theory, and thermodynamics of black holes. Recently, the inter-relations between different types of entropy have been discovered. By synthesizing various aspects of entropy, we thus obtain a deeper understanding of fundamental laws in physics. Now, there is a paper [1], which claims that black hole entropy is obtained as the Noether charge associated with the horizon Killing field. We are then naturally led to ask whether thermodynamic entropy of standard materials is also characterized by a Noether invariant.

In this seminar, we study a classical many-particle system with an external control represented by a time dependent parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation, where trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics [2]. The most remarkable result of our theory is the emergence of a universal constant of the action dimension, while our theory stands on classical mechanics, classical statistical mechanics, and thermodynamics.

Furthermore, we study a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. From unitary time evolution of quantum pure states, we derive an effective action for trajectories in a thermodynamic state space. In the action, the entropy appears with its conjugate variable. Especially, for saddle-point trajectories, the conjugate variable provides a time coordinate called thermal time. Then, the symmetry for the uniform translation of the thermal time emerges, which leads to the entropy as a Noether invariant [3].

[1] R. M. Wald, Phys. Rev. D 48 R3427 (1993).
[2] S. Sasa and Y. Yokokura, Phys. Rev. Lett. 116, 140601 (2016).
[3] S. Sasa, S. Sugiura, and Y. Yokokura, in preparation.

At the nanoscale, the morphological evolution of solid films and islands under annealing is strongly influenced by wetting properties. Inspired by analogies with recent advances in the wetting behavior of liquids, we explore two situations where solid-state wetting plays a crucial role.

In a first part, we discuss the dewetting dynamics of a thin solid film based on 2D Kinetic Monte Carlo (KMC) simulations and analytical models. We focus on the role of the faceting of the dewetting rim, which changes the asymptotic behavior of the dewetting velocity. In addition, we analyze the instability of the dewetting front, which leads to the formation of fingers. We also discuss the consequences of the wetting potential on the dewetting process and on the triple-line dynamics.

In a second part, we will present some results on the wetting statics and dynamics of islands (or nanoparticles) on surface with topographical structures of large aspect ratio, such as pillars or trenches using 3D KMC simulations including elastic effects.

In his landmark 1883 paper, Osborne Reynolds studied qualitatively different kinds of motion of fluid in a straight pipe. His aim was to demonstrate the transition to “sinuous”, in current terminology turbulent, motion as the flow rate increases. As it turns out, he had picked a set up that is practically simple but mathematically very complicated. The flow state that is void of any turbulence remains asymptotically stable for any experimentally reachable flow rate, and swirling flows occur suddenly and intermittently. Their onset is hysteretic and strongly depends on the way the flow rate is varied. Intrigued by this result, A. N. Kolmogorov introduced a more abstract model of fluid motion, restricting it to two spatial dimensions and discarding material boundaries. However, it soon turned out to be overly restrictive and exclude transitions like the one Reynolds had observed. In this presentation, I will show that extending Kolmogorov’s model to three spatial dimensions places it in the same category as elementary shear flows such as that of fluids in pipes and channels. I will study the hysteretic onset of turbulence and the structure of phase space by numerical bifurcation analysis as well as energy methods. This is joint work with Susumu Goto of Osaka University.

In most granular media, interactions between grains are dominated by contact events: either dissipative collisions in diluted granular media or friction in denser ones. I consider grains that carry a magnetic dipole and interact through dipole-dipole interactions. I will discuss how these long range interactions modify the behavior of the granular medium. In particular I will present several instabilities such as the formation of peaks at the surface of a dense granular layer or a transition similar to the liquid-gas phase transition.

Active diffusion, i.e., fluctuating dynamics driven by athermal noise is found in various out-of-equilibrium systems. Here we discuss the nature of the active diffusion of tagged monomers in a flexible polymer. A scaling argument based on the notion of tension propagation clarifies how the polymeric effect is reflected in the anomalous diffusion exponent, which may be of relevance to the dynamics of chromosomal loci in living cells. The idea could be applicable to the behavior of polymers in bacterial suspension as well.

Reference:
T. Sakaue and T. Saito, Soft Matter, 2016, DOI: 10.1039/C6SM00775A

Recent advances in single-cell time-lapse microscopy have revealed large phenotypic heterogeneity at the single-cell level in genetically homogeneous cellular populations. It has been often assumed that such phenotypic noise is evolutionary unimportant because phenotypic differences among cells are not encoded on the stable genetic materials, thus non-heritable. However, the evidences are accumulating that many cellular phenotypes have trans-generational "memories", which might drive clonal cellular populations to quickly and efficiently adapt to harsh environments if the heterogeneous phenotypes are correlated with cellular fitness. Using custom microfluidic single-cell measurement devices, we have recently uncovered several biological roles of phenotypic noise at the single-cell level: (1) Heterogeneity in division interval causes clonal proliferation to grow faster than the constituent single cells on average in constant environments, thus a cellular population can grow faster than cells [1]; and (2) noise in the expression level of a survival-correlated gene allows a fraction of cells in the population to survive and persist during antibiotic drug exposures [2]. Also, our ongoing study have revealed that clonal bacterial populations can acclimatize to drug exposures through multi-generational dynamics, which is enabled by some uncharacterized stable intracellular memory not encoded on genome. In this seminar, I will present the overviews of these studies, and discuss the implications of the results for evolution and genetics.

References:
[1] Hashimoto, M. et al. Noise-driven growth rate gain in clonal cellular populations. Proc. Natl. Acad. Sci. 113, 3251–3256 (2016).
[2] Wakamoto, Y. et al. Dynamic persistence of antibiotic-stressed mycobacteria. Science. 339, 91–5 (2013).

※本セミナーは、講演は日本語、スライドは英語でお願いしてあります。
This seminar will be given in Japanese, but slides are in English.

Fluctuation theorems have attracted considerable attention in the context of statistical mechanics and information thermodynamics. Although integral fluctuation theorems are valid in rather general nonequilibrium situations, they cannot apply to absolutely irreversible processes, where the forward-path probability vanishes and the entropy production diverges in terms of detailed fluctuation theorems. We identify the mathematical origin of this inapplicability as the singularity of probability measure. As a result, we generalize conventional integral fluctuation theorems to absolutely irreversible processes. The new equalities give a more stringent constraint to the average of the entropy production than the conventional second-law-like inequality does.

As a notable application of the new fluctuation theorems, we discuss the Gibbs paradox in small thermodynamic systems. The Gibbs paradox originated from gas mixing, and has raised fundamental problems in thermodynamics and statistical mechanics. Among them, we here consider the consistency between thermodynamic and statistical-mechanical entropies. In this context, the Gibbs paradox is resolved based on the requirement of extensivity in macroscopic thermodynamic systems. However, this resolution cannot apply to small thermodynamic systems because extensivity breaks down. We offer a resolution applicable to small thermodynamic systems based on our fluctuation theorems.

Recent in vivo experiments with optical tracking of particles in living biological cells indicate that active forces strongly dominate thermal Brownian forces in the cellular environment, impacting motion of objects from nanometers to microns in scale. As we show [PNAS 112, E3639 (2015)], such non-thermal fluctuating forces can arise from hydrodynamic stirring of the cytoplasm by various protein machines, enzymes and molecular motors that densely populate the cell. Independent of their specific functions, all such macromolecules are repeatedly changing their conformations and act as oscillating stochastic force dipoles. Numerical estimates reveal that hydrodynamic collective effects of active proteins may account for the experimentally observed dramatic diffusion enhancement in the cytoplasm under ATP supply.

In this talk, I will introduce the new, fast-growing, interdisciplinary field of active matter and present some recent important advances.

Active matter is the term now used by physicists to designate out-of-equilibrium systems in which energy is spent in the bulk, locally, to produce persistent motion/displacement. Examples abound, not just within living systems (bird flocks, fish schools, collective motion of cells, etc.) but also, increasingly, in man-made, well-controlled, non-living systems such as micro- and nano-swimmers, active colloids, in vitro mixtures of biofilaments and motor proteins, etc.

I will show some striking experimental/observational examples and then proceed to give an account of our current understanding of some of the simplest active matter models, which consist of self-propelled particles locally aligning their velocities. In this context, the fluid in which the particles move is neglected, and one speaks of "dry active matter". I will argue that these models do have experimental relevance, in addition to being important per se, much as the Ising model is important in statistical mechanics. I will show that a wealth of new physics arises, which calls for further theoretical studies.

In nature the time trace of a signal might be random however its long time average converges to the corresponding ensemble average (ergodicity). We discuss weak ergodicity breaking a framework introduced by Bouchaud, which describes statistical properties of dynamical systems with power law distributed sojourn times. Examples of blinking quantum dots and diffusion of mRNA in the cell are discussed. The basic question is what is the statistical mechanical framework replacing ordinary statistical mechanics, and the consequence in single particle dynamics.

References:
[1] F. D. Stefani, J. P. Hoogenboom, and E. Barkai, Beyond Quantum Jumps: Blinking Nano-scale Light Emitters, Physics Today, 62, nu. 2, p.34 (February 2009)
[2] E. Barkai, Y. Garini and R. Metzler, Strange Kinetics of Single Molecules in the Cell, Physics Today, 65(8), 29 (2012).