共查询到20条相似文献,搜索用时 31 毫秒
1.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(2):179-208
We study a general class of nonlinear mean field
Fokker-Planck equations in relation with an effective generalized
thermodynamical (E.G.T.) formalism. We show that these equations describe
several physical systems such as: chemotaxis of bacterial
populations, Bose-Einstein condensation in the canonical ensemble,
porous media, generalized Cahn-Hilliard equations, Kuramoto model,
BMF model, Burgers equation, Smoluchowski-Poisson system for
self-gravitating Brownian particles, Debye-Hückel theory of
electrolytes, two-dimensional turbulence... In particular, we show
that nonlinear mean field Fokker-Planck equations can provide
generalized Keller-Segel models for the chemotaxis of
biological populations. As an example, we introduce a new model of
chemotaxis incorporating both effects of anomalous diffusion and
exclusion principle (volume filling). Therefore, the notion of
generalized thermodynamics can have applications for concrete
physical systems. We also consider nonlinear mean field
Fokker-Planck equations in phase space and show the passage from
the generalized Kramers equation to the generalized Smoluchowski
equation in a strong friction limit. Our formalism is simple and
illustrated by several explicit examples corresponding to Boltzmann,
Tsallis, Fermi-Dirac and Bose-Einstein entropies among others. 相似文献
2.
V. Schwämmle E. M.F. Curado F. D. Nobre 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(2):159-165
A recently introduced nonlinear Fokker-Planck equation, derived
directly from a master equation, comes out as a very
general tool to describe phenomenologically systems presenting complex
behavior, like anomalous diffusion, in the presence of
external forces. Such an equation is characterized by a nonlinear diffusion
term that may present, in general, two distinct powers of the probability
distribution. Herein, we calculate the stationary-state distributions
of this equation in some special cases, and introduce associated classes of
generalized entropies in order to satisfy the H-theorem. Within this approach, the parameters associated with the transition
rates of the original master-equation are related to such
generalized entropies, and are shown to obey some restrictions. Some
particular cases are discussed. 相似文献
3.
J.M. Zoido F. Carreño 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(3):459-469
By taking into account a geometrical interpretation of the measurement process [1, 2], we define a set of measures of uncertainty.
These measures will be called geometrical entropies. The amount of information is defined by considering the metric structure in the probability space. Shannon-von Neumann entropy
is a particular element of this set. We show the incompatibility between this element and the concept of variance as a measure
of the statistical fluctuations. When the probability space is endowed with the generalized statistical distance proposed
in reference [3], we obtain the extended entropy. This element, which belongs to the set of geometrical entropies, is fully compatible with the concept of variance. Shannon-von
Neumann entropy is recovered as an approximation of the extended entropy. The behavior of both entropies is compared in the
case of a particle in a square-well potential.
Received 4 November 1999 相似文献
4.
J.-F. Bercher 《Physics letters. A》2011,375(33):2969-2973
We discuss two families of two-parameter entropies and divergences, derived from the standard Rényi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints. 相似文献
5.
G. Baris Bagci 《Physics letters. A》2009,373(36):3230-3234
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptotically for q∈(0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure. 相似文献
6.
T.D. Frank A.R. Plastino 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(4):543-549
A generalized thermostatistics is developed for an entropy measure introduced by Sharma and Mittal. A maximum-entropy scheme
involving the maximization of the Sharma and Mittal entropy under appropriate constraints expressed as escort mean values
is advanced. Maximum-entropy distributions exhibiting a power law behavior in the asymptotic limit are obtained. Thus, results
previously derived for the Renyi entropy and the Tsallis entropy are generalized. In addition, it is shown that for almost
deterministic systems among all possible composable entropies with kernels that are described by power laws the Sharma-Mittal
entropy is the only entropy measure that gives rise to a thermostatistics based on escort mean values and admitting of a partition
function.
Received 27 June 2002 Published online 31 December 2002 相似文献
7.
Two direct methods to calculate fluctuation forces between rigid objects embedded in fluid membranes
The fluctuation-induced attractive interaction of rigid flat objects embedded in a fluid membrane is calculated for a pair
of parallel strips and a pair of equal circular disks. Assuming flat boundary conditions, we derive the interaction from the
entropy of the suppressed boundary angle fluctuation modes. Each mode entropy is computed in two ways: from the boundary angles
themselves and from the mean-curvature mode functions. A formula for the entropy loss of suppressing one or more mean-curvature
modes is developed and applied. For the pair of disks we recover the result of Goulian et al. and Golestanian et al. in a direct manner, avoiding any mappings by Hubbard-Stratonovitch transformations. The mode-by-mode agreement of the two
computed entropies in both systems confirms an earlier claim that mean curvature is the natural measure of integration for
fluid membranes.
Received 15 December 2000 相似文献
8.
A.E. Allahverdyan Th.M. Nieuwenhuizen D.B. Saakian 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(2):317-335
In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are
coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature TJ. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized
two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass
systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T
J
. For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is
an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature
spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation
relation is derived.
Received 12 July 1999 and Received in final form 8 December 1999 相似文献
9.
L. Molgedey W. Ebeling 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(4):733-737
We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea
is that in spite of the high stochasticity in average there might be special local situations where there local order exist
and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series
and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies
and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the
dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the
uncertainty/predictability and the distribution of these quantities.
Received 19 January 2000 相似文献
10.
On the Validations of the Asymptotic Matching Conjectures 总被引:1,自引:0,他引:1
In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies,
which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs. 相似文献
11.
In this paper we recall, extend and compute some information measures for the concomitants of the generalized order statistics (GOS) from the Farlie–Gumbel–Morgenstern (FGM) family. We focus on two types of information measures: some related to Shannon entropy, and some related to Tsallis entropy. Among the information measures considered are residual and past entropies which are important in a reliability context. 相似文献
12.
G. Kaniadakis 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(1):3-13
In ordinary statistical mechanics the Boltzmann-Shannon
entropy is related to the Maxwell-Bolzmann distribution
pi by means of a twofold link. The first link is differential and
is offered by the Jaynes Maximum Entropy Principle. Indeed, the
Maxwell-Boltzmann distribution is obtained by maximizing the Boltzmann-Shannon entropy under
proper constraints. The second link is algebraic and imposes that
both the entropy and the distribution must be expressed in
terms of the same function in direct and inverse form. Indeed, the
Maxwell-Boltzmann distribution pi is expressed in terms of the exponential
function, while the Boltzmann-Shannon entropy is defined as the mean value of
-ln (pi).
In generalized statistical mechanics the second link is customarily
relaxed. Of course, the generalized exponential function defining
the probability distribution function after inversion, produces a
generalized logarithm Λ(pi). But, in general, the mean value
of -Λ(pi) is not the entropy of the system. Here we
reconsider the question first posed in [Phys. Rev. E 66,
056125 (2002) and 72, 036108 (2005)], if and how is it
possible to select generalized statistical theories in which the
above mentioned twofold link between entropy and the distribution
function continues to hold, such as in the case of ordinary
statistical mechanics.
Within this scenario, apart from the standard
logarithmic-exponential functions that define ordinary statistical
mechanics, there emerge other new couples of direct-inverse
functions, i.e. generalized logarithms Λ(x) and generalized
exponentials Λ-1(x), defining coherent and
self-consistent generalized statistical theories. Interestingly, all
these theories preserve the main features of ordinary statistical
mechanics, and predict distribution functions presenting power-law
tails. Furthermore, the obtained generalized entropies are both
thermodynamically and Lesche stable. 相似文献
13.
J. Dong J. F. Teng 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,49(1):129-134
In this paper, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state
with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is
present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And
the formulae for the selection of operations performed by the receiver are given according to the results measured by the
sender and the controller.
相似文献
14.
15.
C. Brunhuber F. G. Mertens Y. Gaididei 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(1):57-65
Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices
were recently generalized to the
case of dispersive long-range interactions (LRI) of the Kac-Baker form.
The variance of the soliton position shows a stronger than linear
time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with
nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons
have algebraic tails instead of
the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar
Langevin equations which hold for the soliton position and width of the two soliton types, the
algebraic solitons reach the superdiffusive long-time limit with a
characteristic t3/2 time-dependence much faster than
exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor
of π smaller for algebraic
solitons. Our results appear to be generic for nonlinear excitaitons in
FPU-chains, because the same superdiffusive time-dependence was also observed in
simulations with discrete breathers. 相似文献
16.
D. Amrath M. Diehl J. P. Lansberg 《The European Physical Journal C - Particles and Fields》2008,58(2):179-192
We study deeply virtual Compton scattering on a virtual pion that is emitted by a proton. Using a range of models for the
generalized parton distributions of the pion, we evaluate the cross section, as well as the beam spin and beam charge asymmetries
in the leading-twist approximation. Studying Compton scattering on the pion in suitable kinematics puts high demands on both
beam energy and luminosity, and we find that the corresponding requirements will first be met after the energy upgrade at
Jefferson Laboratory. As a by-product of our study, we construct a parameterization of pion generalized parton distributions
that has a non-trivial interplay between the x and t dependence and is in good agreement with form factor data and lattice calculations. 相似文献
17.
Robson P. Bonidia Anderson P. Avila Santos Breno L. S. de Almeida Peter F. Stadler Ulisses Nunes da Rocha Danilo S. Sanches Andr C. P. L. F. de Carvalho 《Entropy (Basel, Switzerland)》2022,24(10)
In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. 相似文献
18.
We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations.
In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number
of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with
a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii)
a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent
dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision
model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer
collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision
we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions
with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated
by a net translational motion of the two-chain system. 相似文献
20.
V. Kumar 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,24(1-3):227-232
We report the recent findings of metal (M) encapsulated
clusters of silicon from computer experiments based on
ab initio total energy
calculations and a cage shrinkage and atom removal approach. Our
results show that using a guest atom, it is possible to wrap
silicon in fullerenelike (f)
structures, as sp2 bonding is not
favorable to produce empty cages unlike for carbon. Transition M
atoms have a strong bonding with the silicon cage that are
responsible for the compact structures. The size and structure
of the cage change from 14 to 20 Si atoms depending upon the
size and valence of the M atom. Fewer Si atoms lead to
relatively open structures. We find cubic,
f, Frank-Kasper (FK)
polyheral type, decahedral, icosahedral and hexagonal structures
for M@Sin with n = 12-16 and several different M
atoms. The magic behavior of 15 and 16 atom Si cages is in
agreement with experiments. The FK polyhedral cluster,
M@Si16 has an exceptionally large density
functional gap of about 2.35 eV calculated within the
generalized gradient approximation. It is likely to give rise to
visible luminescence in these clusters. The cluster-cluster
interaction is weak that makes such clusters attractive for
cluster assembled materials. Further studies to stabilize
Si20 cage with M = Zr, Ba, Sr, and Pb
show that in all cases there is a distortion of the
f cage. Similar studies on M
encapsulated germanium clusters show FK polyhedral and
decahedral isomers to be more favorable. Also perfect
icosahedral M@Ge12 and
M@Sn12 clusters have been obtained with
large gaps by doping with divalent M atoms. Recent results of
the H interaction with these clusters, hydrogenated silicon
fullerenes as well as assemblies of clusters such as nanowires
and nanotubes are briefly presented. 相似文献