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1.
In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated
to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute
the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second
part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, 'aperiodic'
orbits (chaotic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique
provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important
to remark that this method is very simple to compute and does not require long time integrations, just realistic physical
times.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model. 相似文献
3.
A. W. Strong 《Experimental Astronomy》1995,6(4):97-102
The Maximum Entropy method is a practical technique for generating intensity skymaps from Compton-telescope data. The application of the method to COMPTEL data for point sources and large-scale emission is described. New developments in the method are illustrated. 相似文献
4.
Manfred P. Leubner 《Astrophysics and Space Science》2002,282(3):573-579
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails.
The high energy particle populations are accurately represented by the family of kappa-distributions where the use of these
distributions has been unjustly criticized because of a perceived lack of theoretical justification. We show that distributions
very close to kappa-distributions are a consequence of the generalized entropy favored by non extensive statistics, which
provides the missing link for power-law models of non-thermal features from fundamental physics. With regard to the physical
basis supplied by the Tsallis nonextensive entropy formalism we propose that this slightly modified functional form, qualitatively
similar to the traditional kappa-distribution, be used in fitting particle spectra in the future. 相似文献
5.
汪定雄 《中国天文和天体物理学报》1991,(1)
在黑洞蒸发的最后阶段其残余质量为Planck质量的量级,因而所对应的黑洞熵为2πk_B量级,在Bekenstein工作的基础上作者导出在吸积物质的过程中黑洞的最小熵增为2πk_B,这一最小熵增又限制能参与吸积物质的黑洞的质量下限为Planck质量的量级,因而所对应的最小黑洞熵也为2πk_B这一量级。作者进一步指出:黑洞的最小熵及最小熵增不受引力常数G变化的影响,因此上述结论在极早期宇宙中也能成立,在上述分析的基础上作者提出一个猜想:黑洞熵可以量子化,其量子单位为2πk_B。 相似文献
6.
7.
With the increasing of applications of Global Positioning System (GPS), the research on the factors affecting the radio signals is becoming more and more important. One of the most significant effects on ionosphere monitoring is the ionospheric radio occultation (IRO), and the IRO data is now serving as one of the most important monitoring sources for the ionospheric measurements. Meanwhile the inversion of the occultation data is a popular topic. The traditional Abel inversion process through compensated total electron content (TEC) is a linear inversion method, thus it would transfer the measurement errors directly to the inversion results. In order to improve the occultation results, we introduce in this paper two nonlinear methods, namely the regularization method and the maximum entropy regularization method. Through designed simulative experiments, we verify and compare these three methods, and conclude that the maximum entropy regularization method can reduce significantly the influence of measurement errors. 相似文献
8.
In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological
models with bouncing behavior such as chameleon cosmology where the boundary of the universe is assumed to be enclosed by
the dynamical apparent horizon. From a thermodynamic point of view, to link between thermodynamic and geometric parameters
in cosmological models, we introduce “entropy rate of change multiplied by the temperature” as a model independent thermodynamic
state parameter together with the well known {r,s} statefinder to differentiate the dark energy models. 相似文献
9.
10.
11.
汪定雄 《中国天文和天体物理学报》1996,(1)
本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程，计算了约束在一个球形盒子中的目引力辐射体系的墙（不含中心黑洞和含有中心黑洞两种情况）．与Sorkin等人的计算比较，本文的结果不会出现发散困难，而且体系的总摘（包括中心黑洞的墙）的上阳正好等于坍缩后形成的同质量的黑洞嫡．作者认为，自引力辐射体系坍绩的合理模式是先形成中心黑洞，然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞．在坍缩过程中，任一中间态的媳总是比末态的黑洞墙小，到坍缩过程结束总熵才等于对应的黑洞摘．这一结果为黑洞滴的起源提供了一个合理的解释． 相似文献
12.
14.
The work compiles a correlated study of a gravitational quasi equilibrium thermodynamic approach for establishing and signifying a unique behavior of the cosmological entropy and phase transitions in an expanding Universe. On the basis of prescribed boundary conditions for the cluster temperature a relation for the intra‐cluster medium (ICM) of galaxy clusters has been derived. A more productive and signifying approach of the correlation functions used for galaxy clustering phenomena shows a unique behavior of the entropy change where a phenomenon known as the gravitational phase transition occurs. This unique behavior occurs with a symmetry breaking from mild clustering to low clustering and from mild clustering to high clustering which differs from a normal symmetry breaking in material sciences. We also derive results for the specific latent heat associated with the phase transitions of 3.20 Tc and 0.55 Tc for the mildly clustered phase to the low clustered phase and from the mildly clustered phase to the highly clustered phase, respectively. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Constantino Tsallis 《Astrophysics and Space Science》2006,305(3):261-271
The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies S
BG
≡ −k ∑
i = 1
W
p
i
ln p
i
and S
q
≡ k (1−∑
i = 1
W
p
i
q
)/(q−1) (q∊ℜ S
1 = S
BG
). Through them we revisit the concept of additivity, and illustrate the (not always clearly perceived) fact that (thermodynamical) extensivity has a well defined sense only if we specify the composition law that is being assumed for the subsystems (say A and B). If the composition law is not explicitly indicated, it is tacitly assumed that A and B are statistically independent. In this case, it immediately follows that S
BG
(A+B) = S
BG
(A)+S
BG
(B), hence extensive, whereas S
q
(A+B)/k = [S
q
(A)/k]+[S
q
(B)/k]+(1−q)[S
q
(A)/k][S
q
(B)/k], hence nonextensive for q ≠ 1. In the present paper we illustrate the remarkable changes that occur when A and B are specially correlated. Indeed, we show that, in such case, S
q
(A+B) = S
q
(A)+S
q
(B) for the appropriate value of q (hence extensive), whereas S
BG
(A+B) ≠ S
BG
(A)+S
BG
(B) (hence nonextensive). We believe that these facts substantially improve the understanding of the mathematical need and physical origin of nonextensive statistical mechanics, and its interpretation in terms of effective occupation of the W
a priori available microstates of the full phase space. In particular, we can appreciate the origin of the following important fact. In order to have entropic extensivity (i.e., lim
N→∞
S(N)/N < ∞, where N≡ numberof
elements
of
the
system), we must use (i) S
BG
, if the number W
eff of effectively occupied microstates increases with N like W
{{eff}}∼ W ∼ μ
N
(μ ≥ 1); (ii) S
q
with q = 1−1/ρ, if W
{{eff}}∼ N^ρ < W (ρ ≥ 0). We had previously conjectured the existence of these two markedly different classes. The contribution of the present paper is to illustrate, for the first time as far as we can tell, the derivation of these facts directly from the set of probabilities of the W microstates. 相似文献
16.
17.
Q. A. Wang 《Astrophysics and Space Science》2006,305(3):273-281
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics.We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures. 相似文献
18.
1 INTRODUCTIONIn theoretical physics, the thermodynamics of blajck holes remains an enigma, it turns outto be a junction of general relativity) quantum mechanics, and statistical physics.Since Bekenstein and Hawking proposed, in 1970s, that the black hole eatropy is proportional to the area of the event horizon (Bekenstein 1972, 1973, 1974; Hawking 1975; Kalloshet al. 1993), many efforts are devoted to the study of the statistical origin of the black holeentropy)One such effort is the wi… 相似文献
19.
20.
运用在brick-wall方法的基础上发展起来的薄膜模型计算了六维动态黑洞的自由能和玻色子熵，然后应用Г矩阵方法计算了费米子熵．结果显示六维动态黑洞的玻色子熵和费米子熵有相同的形式，它们之间只相差一个系数．并且仍然满足Bekenstein-Hawking的熵与面积的关系． 相似文献