This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.
The concept of weak invariants has recently been introduced in the context of conserved quantities in finite-time processes in nonequilibrium quantum thermodynamics. A weak invariant itself has a time-dependent spectrum, but its expectation value remains constant under time evolution defined by a relevant master equation. Although its expectation value is thus conserved by definition, its fluctuation is not. Here, time evolution of such a fluctuation is studied. It is shown that if the subdynamics is given by a completely positive map, then the fluctuation of the associated weak invariant does…
The thermodynamic relations in the Tsallis statistics were studied with physical quantities. An additive entropic variable related to the Tsallis entropy was introduced by assuming the form of the first law of the thermodynamics. The fluctuations in the Tsallis statistics were derived with physical quantities with the help of the introduced entropic variable. It was shown that the mean squares of the fluctuations of the physical quantities in the Tsallis statistics are the same as those in the conventional statistics. The mean square of the fluctuation of the Tsallis entropy and the mean squar…
We provide a detailed investigation on the fluctuations of the currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also investigate full counting statistics of the two currents and show that fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.
Energy distribution and energy fluctuation in Tsallis statistics
用OLM方法研究了Tsallis正则系综的能量分布和能量涨落。所得的能量涨落公式与前人的工作[Liu L.Y.和杜J.L. Physica A 387（2008）5417]。在讨论理想气体的应用时，我们发现在热力学极限下，能量涨落是不可忽略的，这表明在Tsallis统计中，这种情况是系综不等价的。我们研究了Plastino和Plastino [Phys. Lett. A 193（1994）140]，用于描述与有限卫生浴接触的系统。在这种情况下，能量涨落的两个公式是等价的，而非广延参数q起着非常重要的作用。
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given population bottleneck remain poorly understood. In this context, we show that long-term post-bottleneck outcomes can depend crucially on the rate at which a diminished population grows whilst recovering. That is, two otherwise identical populations, each having undergone the same bottleneck, can fixate on dramatically different demographics due to different rates…
We discuss the surprising connection between turbulent circulation statistics and minimal surfaces, as recently established by Iyer et al. [Proc. Nat. Acad. Sci. U.S.A. 118(43), e2114679118 (2021)].
We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in closed compact forms so as to treat the adiabatic and nonadiabatic contributions systematically. We derive the fluctuation theorem by taking into account the time reversal symmetry and the property that the instantaneous currents flowing into the left and the right reservoir are not equal. It is found that the fluctuation-dissipation relation derived from the …
We derive the fluctuation-dissipation relation and explore its connection with the equipartition theorem and Maxwell-Boltzmann statistics through the use of different stochastic analytical techniques. Our first approach is the theory of backward stochastic differential equations, which arises naturally in this context, and facilitates the understanding of the interplay between these classical results of statistical mechanics. The second approach consists in deriving forward stochastic differential equations for the energy of an electric system according to both Itô and Stratonovich stochastic …
