The kinetic gas universe

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However, when the gravitational field of a kinetic gas is derived via the Einstein-Vlasov equations, the information about the velocity distribution of the gas particles is averaged out and therefore lost. We propose to derive the gravitational field of a kinetic gas directly from its 1PDF, taking the velocity distribution fully into account. We conjecture that this refined approach could possibly account for the observed dark energy phenomenology.

Oscillatory-Precessional Motion of a Rydberg Electron Around a Polar Molecule

We provide a detailed classical description of the oscillatory-precessional motion of an electron in the field of an electric dipole. Specifically, we demonstrate that in the general case of the oscillatory-precessional motion of the electron (the oscillations being in the meridional direction (θ-direction) and the precession being along parallels of latitude (φ-direction)), both the θ-oscillations and the φ-precessions can actually occur on the same time scale—contrary to the statement from the work by another author. We obtain the dependence of φ on θ, the time evolution of the dynamical variable θ, the period Tθ of the θ-oscillations, and the change of the angular variable φ during one half-period of the θ-motion—all in the forms of one-fold integrals in the general case and illustrated it pictorially. We also produce the corresponding explicit analytical expressions for relatively small values of the projection pφ of the angular momentum on the axis of the electric dipole. We also derive a general condition for this conditionally-periodic motion to become periodic (the trajectory of the electron would become a closed curve) and then provide examples of the values of pφ for this to happen. Besides, for the particular case of pφ = 0 we produce an explicit analytical result for the dependence of the time t on θ. For the opposite particular case, where pφ is equal to its maximum possible value (consistent with the bound motion), we derive an explicit analytical result for the period of the revolution of the electron along the parallel of latitude.

Some aspects of the inertial spin model for flocks and related kinetic equations

In this paper, we study the macroscopic behavior of the inertial spin (IS) model. This model has been recently proposed to describe the collective dynamics of flocks of birds, and its main feature is the presence of an auxiliary dynamical variable, a sort of internal spin, which conveys the interaction among the birds with the effect of better describing the turning of flocks. After discussing the geometrical and mechanical properties of the IS model, we show that, in the case of constant interaction among the birds, its mean-field limit is described by a nonlinear Fokker–Planck equation, whose equilibria are fully characterized. Finally, in the case of non-constant interactions, we derive the kinetic equation for the mean-field limit of the model in the absence of thermal noise, and explore its macroscopic behavior by analyzing the mono-kinetic solutions.

Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies

We study the emergent dynamics of the thermomechanical Cucker–Smale (TCS) model with switching network topologies. The TCS model is a generalized CS model with extra internal dynamical variable called “temperature” in which isothermal case exactly coincides with the CS model for flocking. In previous studies, emergent dynamics of the TCS model has been mostly restricted to some static network topologies such as complete graph, connected graph with positive in and out degrees at each node, and digraphs with spanning trees. In this paper, we consider switching network topologies with a spanning tree in a sequence of time-blocks, and present two sufficient frameworks leading to the asymptotic mono-cluster flocking in terms of initial data and system parameters. In the first framework in which the sizes of time-blocks are uniformly bounded by some positive constant, we show that temperature and velocity diameters tend to zero exponentially fast, and spatial diameter is uniformly bounded. In the second framework, we admit a situation in which the sizes of time-blocks may grow mildly by a logarithmic function. In latter framework, our temperature and velocity diameters tend to zero at least algebraically slow.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

Numerical and analytical analyses of a matrix model with non-pairwise contracted indices

We study a matrix model that has $$\phi _a^i\ (a=1,2,\ldots ,N,\ i=1,2,\ldots ,R)$$ϕai(a=1,2,…,N,i=1,2,…,R) as its dynamical variable, whose lower indices are pairwise contracted, but upper ones are not always done so. This matrix model has a motivation from a tensor model for quantum gravity, and is also related to the physics of glasses, because it has the same form as what appears in the replica trick of the spherical p-spin model for spin glasses, though the parameter range of our interest is different. To study the dynamics, which in general depends on N and R, we perform Monte Carlo simulations and compare with some analytical computations in the leading and the next-leading orders. A transition region has been found around $$R\sim N^2/2$$R∼N2/2, which matches a relation required by the consistency of the tensor model. The simulation and the analytical computations agree well outside the transition region, but not in this region, implying that some relevant configurations are not properly included by the analytical computations. With a motivation coming from the tensor model, we also study the persistent homology of the configurations generated in the simulations, and have observed its gradual change from $$S^1$$S1 to higher dimensional cycles with the increase of R around the transition region.

Self-adjoint time operator of a quantum field

We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys the Klein–Gordon equation and Schrödinger equation. The energy observed is quantized under the constraint that a particle’s mass is on shell. This real scalar field has the same properties of a zero-spin bosonic field. Furthermore, the internal time of this system can be represented by a self-adjoint operator without contradicting the Pauli’s theorem. Neutrino can be an interesting candidate for investigating the effects of these temporal and spatial vibrations because of its extremely light weight.

Gravity and quantum theory: Domains of conflict and contact

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer-dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first-principles will require the dynamical principles of the theory to be invariant under the shift [Formula: see text]. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry [Formula: see text], they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

Temperature–Energy-space Sampling Molecular Dynamics: Deterministic, Iteration-free, and Single-replica Method utilizing Continuous Temperature System

We developed coupled Nosé–Hoover (NH) molecular dynamics equations of motion (EOM), wherein the heat-bath temperature for the physical system (PS) fluctuates according to an arbitrary predetermined weight. The coupled NH is defined by suitably jointing the NH EOM of the PS and the NH EOM of the temperature system (TS), where the inverse heat-bath temperature β is a dynamical variable. In this study, we define a method to determine the effective weight for enhanced sampling of the PS states. The method, based on ergodic theory, is reliable, and eliminates the need for time-consuming iterative procedures and resource-consuming replica systems. The resulting TS potential in a two dimensional (β, ϵ)-space forms a valley, and the potential minimum path forms a river flowing through the valley. β oscillates around the potential minima for each energy ϵ, and the motion of β derives a motion of ϵ and receives the ϵ’s feedback, which leads to a mutual boost effect. Thus, it also provides a specific dynamical mechanism to explain the features of enhanced sampling such that the temperature-space “random walk” enhances the energy-space “random walk.” Surprisingly, these mutual dynamics between β and ϵ naturally arise from the static probability theory formalism of double density dynamics that was previously developed, where the Liouville equation with an arbitrarily given probability density function is the fundamental polestar. Numerical examples using a model system and an explicitly solvated protein system verify the reliability, simplicity, and superiority of the method.

Automated, predictive, and interpretable inference of Caenorhabditis elegans escape dynamics

The roundworm Caenorhabditis elegans exhibits robust escape behavior in response to rapidly rising temperature. The behavior lasts for a few seconds, shows history dependence, involves both sensory and motor systems, and is too complicated to model mechanistically using currently available knowledge. Instead we model the process phenomenologically, and we use the Sir Isaac dynamical inference platform to infer the model in a fully automated fashion directly from experimental data. The inferred model requires incorporation of an unobserved dynamical variable and is biologically interpretable. The model makes accurate predictions about the dynamics of the worm behavior, and it can be used to characterize the functional logic of the dynamical system underlying the escape response. This work illustrates the power of modern artificial intelligence to aid in discovery of accurate and interpretable models of complex natural systems.