A possible deformed algebra and calculus inspired in nonextensive thermostatistics
نویسنده
چکیده
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.
منابع مشابه
Generalized symmetric nonextensive thermostatistics and q-modified structures
We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q ↔ q−1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed. PACS: 05.20.-y; 0...
متن کاملNonlinear Wave Equations Related to Nonextensive Thermostatistics
We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein–Gordon, and Dirac wave equations. These previously introduced equati...
متن کاملBasic-deformed Thermostatistics
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a qnonuniform lattice we introduce the basic-entropy related to the basic-exponential by means of a q-variational principle. Remarkably, this distribution exhibits a nat...
متن کاملContinuity of κ-deformed entropies and relative entropies
A large class of entropy functions and corresponding relative entropies is considered. Inequalities are derived, proving continuity with respect to specific distance functions. As an application it is shown that these entropies satisfy Lesche’s continuity condition. The entropies of Tsallis’ nonextensive thermostatistics are taken as examples.
متن کاملContinuity of a class of entropies and relative entropies
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche’s stability condition. The entropies of Tsallis’ nonextensive thermostatistics are taken as exam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003