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Microscopic speed limits that constrain the motion of matter, energy, and information abound in physics, from the "ultimate" speed limit set by light to Lieb-Robinson speed limits in quantum spin systems. In addition to these state-independent speed limits, systems can also be governed by emergent state-dependent speed limits indicating slow dynamics arising, for example, from slow low-energy quasiparticles. Here we describe a different kind of speed limit: a situation where complex information/entanglement spreads rapidly, in a fashion inconsistent with any speed limit, but where simple signals continue to obey an approximate speed limit. If we take the point of view that the motion of simple signals defines the local spacetime geometry of the universe, then the effects we describe show that spacetime locality can be compatible with a high degree of non-local interactions provided these are sufficiently chaotic. With this perspective, we sharpen a puzzle about black holes recently raised by Shor and propose a schematic resolution., 38 pages

In order to evaluate and compare the accurate activation energy variations of two kinds of deposited clays (i.e. non-organic clay and organic clay), thermo-gravimetric analysis (TGA) was firstly conducted to study the reaction characteristics of the two clay samples. Two periods of weight losses were observed according to each TGA curve for both clay samples. The first period happened due to water evaporation, while the second period was mainly caused by the composition reactions of clay minerals, especially influenced by the de-hydroxylation of kaolinite. An obvious phenomenon is that the organic clay with a high soil organic matter (SOM) has a higher activity energy. Then, four common kinetics models [i.e. the Coats-Redfern method, the Doyle integral method, the maximum rate method, and the distributed activation energy model (DAEM)] were used to calculate and compare the activation energy values. And the Doyle integral method and the DAEM method are considered as two recommended models to analyze the activation energy performance during thermal treatment. Some interesting conclusions can be summarized as: (1) The multi-period reactions of deposited clays during the heating process are common, especially for organic clay. It would be beneficial knowing its biomass resource feasibility concerning the second weight loss; (2) The high SOM has a significant influence on the potential energy unitization of deposited clays, while the variations of activity energy for deposited clays are influenced by the mineral compositions and microstructure features; (3) It is possible to evaluate the accurate activity energy of deposited clays combined with TGA tests and two recommended models (i.e. the Doyle integral method and DAEM method).

Fatty acid production from Chlorella vulgaris under nitrogen starvation in autotrophic, heterotrophic, and mixotrophic cultures was investigated and compared in this study. Both the biomass and fatty acid productivities of mixotrophic algal cells exceed the combination of autotrophic and heterotrophic cells when acetate was adopted as the organic carbon source, and fatty acid productivity from mixotrophic culture (130 mg L−1 day−1) is 1.9 times greater than the combination of autotrophic (15 mg L−1 day−1) and heterotrophic (51 mg L−1 day−1) cultures. C18:1 is the predominant fatty acid accounting for 60.4 and 64.5% of the total fatty acids in the mixotrophic and heterotrophic cultures, respectively. Moreover, the fatty acid yield from mixotrophic culture is almost two times greater than from heterotrophic culture. Proteomic analysis revealed that the activity of the tricarboxylic acid (TCA) cycle is improved in mixotrophic culture when compared with heterotrophic culture, leading to more fatty acid synthesis in C. vulgaris.

We study the time evolution of R\'enyi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The R\'enyi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of R\'enyi entropy, respectively., Comment: 33 pages

In this paper, we present a new method of fractional dynamics, i.e., the fractional Mei symmetrical perturbation method of a disturbed system, and explore the adiabatic invariant directly led by the perturbation. For a dynamical system which is disturbed by small forces of perturbation, the disturbed fractional generalized Hamiltonian equation is investigated and, under a more general kind of fractional infinitesimal transformation of a Lie group, the fractional Mei symmetrical definition and determining equation of a disturbed dynamical system are given; then, the determining equation of fractional Mei symmetrical perturbation is obtained. In particular, we present the fractional Mei symmetrical perturbation method of a disturbed dynamical system and it is found that, using the new method, we can find a new kind of non-Noether adiabatic invariant directly led by the perturbation. As special cases, we obtain a new fractional Mei symmetrical conservation law of the undisturbed dynamical system and a Mei symmetrical perturbation theorem of the disturbed integer dynamical system. Also, as the fractional Mei symmetrical perturbation method’s applications, we find the adiabatic invariants of a disturbed fractional Duffing oscillator and a disturbed fractional Lotka biochemical oscillator. This work constructs a basic theoretical framework of fractional Mei symmetrical perturbation method and provides a general method of fractional dynamics.

In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method’s applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry.

In this paper, we reveal the uncertainty and its fractional generalized Hamiltonian representation for the fractional and nonlinear problem and find general methods of constructing a family of fractional dynamical models. By using the definition of combined fractional derivative, we construct a unified fractional generalized Hamiltonian equation, a fractional generalized Hamiltonian equation with combined Riemann–Liouville derivative, and a fractional generalized Hamiltonian equation with combined Caputo derivative; also, as special cases, under the different definitions of fractional derivatives, we, respectively, obtain a series of different kinds of fractional generalized Hamiltonian equations. In particular, we present a new concept of the family of fractional dynamical models, and it is found that, using the fractional generalized Hamiltonian method, we can construct a series of families of fractional dynamical models. And then, as the new method’s application, we construct three new kinds of families of fractional dynamical models, which include a family of fractional Lorentz–Dirac models, a family of fractional Lotka–Volterra models and a family of fractional Henon–Heiles models.

In this paper, we present a new type of fractional Lie symmetrical method for finding conserved quantities and explore its applications. For the fractional generalized Hamiltonian system, we introduce a new kind of single-parameter fractional infinitesimal transformation of Lie group in α−1 order space and, under this transformation, give the invariance of the fractional dynamical system and the fractional Lie symmetrical determining equation. Further, a number of important relationships of the fractional Lie symmetrical method are investigated, which reveal the interior properties of the system. By using these relationships, a fractional Lie symmetrical basic integral variable relation and a new fractional Lie symmetrical conservation law are presented. The new conserved quantity is constructed base on fractional Lie symmetrical infinitesimal generators and the interior properties of the system itself, without solving the complicated structural equation. Furthermore, the fractional Lie symmetrical method is applied to the fractional generalized Hamiltonian system of even dimensions. Also, as the new fractional Lie symmetrical method’s applications, we respectively find the conserved quantities of a fractional Duffing oscillator model and a fractional Lotka biochemical oscillator model.

In this paper, we present a general method of finding conserved quantities, i.e., fractional Jacobi last multiplier method, and explore its applications to fractional dynamical system. Based on the definition of Riesz–Riemann–Liouville fractional derivative, we study general fractional dynamical equations, construct its fractional Jacobi last multiplier, and, respectively, give the determining equation and three important properties of the multiplier. And then, we present the fractional Jacobi last multiplier method, which includes three theorems of finding conserved quantities of fractional dynamical systems. Further, in fractional framework, we explore the relation between Lie symmetry and Jacobi last multiplier. Furthermore, the fractional Jacobi last multiplier method is applied to the fractional generalized Hamiltonian system, the complete fractional Hamiltonian system, the standard fractional Hamiltonian system, the fractional Nambu system and the fractional Birkhoffian system, and five corresponding propositions are given. Also by using the fractional Jacobi last multiplier method, we respectively find the conserved quantities of a fractional relativistic Buchdahl model, a fractional Euler–Poinsot model and a fractional Duffing oscillator model. This work constructs a basic theoretical framework of fractional Jacobi last multiplier method, and provides a general method of fractional dynamics.

In this paper, we present the fractional Mei symmetrical method of finding conserved quantity and explore its applications to physics. For the fractional generalized Hamiltonian system, we introduce the fractional infinitesimal transformation of Lie groups and, under the transformation, give the fractional Mei symmetrical definition, criterion and determining equation. Then, we present the fractional Mei symmetrical theorem of finding conserved quantity. As the fractional Mei symmetrical method’s applications, we respectively find the conserved quantities of a fractional general relativistic Buchduhl model, a fractional three-body model and a fractional Robbins–Lorenz model.

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.