首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 203 毫秒
1.
Ao P 《理论物理通讯》2008,49(5):1073-1090
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.  相似文献   

2.
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we show that even in well-mixed finite populations, where the dynamics is inherently stochastic, biodiversity is possible with three cyclic-dominant strategies. We show how the interplay of evolutionary dynamics, discreteness of the population, and the nature of the interactions influences the coexistence of strategies. We calculate a critical population size above which coexistence is likely.  相似文献   

3.
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α < 2, the power law decay with large exponent ( α > 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement. Received 29 July 2000 and Received in final form 25 September 2000  相似文献   

4.
In a previous paper (Duncan, T.L., Semura, J.S. in Entropy 6:21, 2004) we considered the question, “What underlying property of nature is responsible for the second law?” A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second law. This line of thinking highlights the existence of two independent but coupled sets of laws: Information dynamics and energy dynamics. The distinction helps shed light on certain foundational questions in statistical mechanics. For example, the confusion surrounding previous “derivations” of the second law from energy dynamics can be resolved by noting that such derivations incorporate one or more assumptions that correspond to the loss of information. In this paper we further develop and explore the perspective in which the second law is fundamentally a law of information dynamics.  相似文献   

5.
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.  相似文献   

6.
Abhijit Kar Gupta 《Physica A》2012,391(4):1509-1514
This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called ‘feedback’ was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of ‘fitness’ and ‘selection’ in the present model of economic evolution.  相似文献   

7.
8.
An analytical representation of a random process with independent increments in some space (random walks introduced by Pearson) is considered. The law of random walk distribution in space is derived from the general representation of stochastic elementary hops (distribution law of hop probability) using Kadanoff’s concept of the unit increment as one hop. For limited hop laws and laws of hop distributions with all moments there naturally arises Chandrasekhar’s result that describes ordinary physical diffusion. For laws of hop distributions without the second and highest moments there also arise known Lévy walks (flights) sometimes treated as superdiffusion. For the intermediate case, where the distributions of hops have at least the second moment and not all finite moments (these hops are sometimes called truncated Lévy walks), the asymptotic form of the random walk distribution was obtained for the first time. The results obtained are compared with the experimental laws known in econophysics. Satisfactory agreement is observed between the developed theory and the empirical data for insufficiently studied truncated Lévy walks.  相似文献   

9.
We provide the link between population dynamics and the dynamics of Darwinian evolution via studying the joint population dynamics of similar populations. Similarity implies that the relative dynamics of the populations is slow compared to, and decoupled from, their aggregated dynamics. The relative dynamics is simple, and captured by a Taylor expansion in the difference between the populations. The emerging evolution is directional, except at the singular points of the evolutionary state space. Here "evolutionary branching" may occur. The diversification of life forms thus is demonstrated to be a natural consequence of the Darwinian process.  相似文献   

10.
We present a detailed analysis of the -relaxation dynamics of a simple glass former, a binary Lennard-Jones system with a stochastic dynamics. By testing the various predictions of mode-coupling theory, including the recently proposed corrections to the asymptotic scaling laws, we come to the conclusion that in this time regime the dynamics is described very well by this theory. Received 5 February 1999 and Received in final form 7 June 1999  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号