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Rajagopal,Macroscopic thermodynamics of equilibrium characterized by powerlaw canonical distributions
"... Macroscopic thermodynamics of equilibrium is constructed for systems obeying powerlaw canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is complementary to the Gibbs theorem for the celebrated expone ..."
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Macroscopic thermodynamics of equilibrium is constructed for systems obeying powerlaw canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is complementary to the Gibbs theorem for the celebrated exponential canonical distributions of systems in contact with a heat bath. Thereby, a thermodynamic basis is provided for powerlaw phenonema ubiquitous in nature. PACS numbers: 05.20.y Classical statistical mechanics 05.70.a Thermodynamics 1 Statistical mechanics builds an essential bridge between the laws of nature governing microscopic dynamics of constituents of matter and its macroscopic behavior. One and only example of such a description known to date is the theory of Boltzmann and Gibbs characterized by the exponential distributions. Since many systems fall under the sway of this theory, there has been no attempt to find alternate possibilities. However, nowadays it is widely recognized that many phenomena in nature obey different kinds of distributions, i.e., the powerlaw distributions. We may cite here a few such
Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches, Funct
 Anal. Appl
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Action principle and Jaynes’ guess method
"... A path information is defined in connection with the probability distribution of paths of nonequilibrium hamiltonian systems moving in phase space from an initial cell to different final cells. On the basis of the assumption that these paths are physically characterized by their action, we show that ..."
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A path information is defined in connection with the probability distribution of paths of nonequilibrium hamiltonian systems moving in phase space from an initial cell to different final cells. On the basis of the assumption that these paths are physically characterized by their action, we show that the maximum path information leads to an exponential probability distribution of action which implies that the most probable paths are just the paths of stationary action. We also show that the averaged (over initial conditions) path information between an initial cell and all the possible final cells can be related to the entropy change defined with natural invariant measures for dynamical systems. Hence the principle of maximum path information suggests maximum entropy and entropy change which, in other words, is just an application of the action principle of classical mechanics to the cases of stochastic or instable dynamics. 1
Classes of NDimensional Nonlinear FokkerPlanck Equations Associated to Tsallis Entropy
 ENTROPY
, 2011
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The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks
 ENTROPY
, 2011
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Signatures of discrete scale invariance in Dst time series
 Entropy 2013
"... [1] Self‐similar systems are characterized by continuous scale invariance and, in response, the existence of power laws. However, a significant number of systems exhibits discrete scale invariance (DSI) which in turn leads to log‐ periodic corrections to scaling that decorate the pure power law. Her ..."
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[1] Self‐similar systems are characterized by continuous scale invariance and, in response, the existence of power laws. However, a significant number of systems exhibits discrete scale invariance (DSI) which in turn leads to log‐ periodic corrections to scaling that decorate the pure power law. Here, we present the results of a search of log‐periodic corrections to scaling in the squares of Dst index increments which are taken as proxies of the energy dissipation rate in the magnetosphere. We show that Dst time series exhibit DSI and discuss the consequence of this feature, as well as the possible implications of Dst DSI on space weather
Risk aversion in financial decisions: A nonextensive approach ∗
, 2003
"... The sensitivity to risk that most people (hence, financial operators) feel affects the dynamics of financial transactions. Here we present an approach to this problem based on a current generalization of BoltzmannGibbs statistical mechanics. An important question in the theory of financial decision ..."
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The sensitivity to risk that most people (hence, financial operators) feel affects the dynamics of financial transactions. Here we present an approach to this problem based on a current generalization of BoltzmannGibbs statistical mechanics. An important question in the theory of financial decisions is how to take into account those psychological attitudes of human beings that produce significant deviations from the ideally rational behavior. It is not by chance that a new discipline that focus on such questions, behavioral finance, is starting to gain universal recognition. In fact, Daniel Kanheman