Continuous Distribution Of Tsallis Entropy And Its Applications

As the Boltzmann Gibbs-entropy is more and more extensive and successful application, in order to solve more practical problems, people begin to pay close attention to all kinds of general entropy. Tsallis entropy was based on the Boltzmann Gibbs theory, and successfully applied in physics, chemistry, biology, medicine, economy, various fields of geophysics and so on. The paper arrive at some conclusions about Tsallis entropy and the Tsallis entropy in continue distribution.Firstly, this paper introduces the entropy and some generalized entropy based on the background of entropy, and use Renyi entropy to prove the famous Hadamard inequalities. Then the paper also introduces some practical applications of Tsallis entropy.From the second part of this article, we firstly introduce some properties of Tsallis entropy and Tsallis relative entropy, these properties will be used in follow-up studies.To extend the property of Tsallis entropy, we build the equation between the Renyi entropy and the Tsallis entropy.Secondly, we deduce the Tsallis relative entropy expression of some common continuous distribution,including univariate and multivariate, according to the relationship between Tsallis entropy and exponential distribution.These results are summarized in Table2-2. These conclusions have a wide range of applications in statistics and information theory.Lately, the paper introduces the relationship between Tsallis entropy and the Tsallis relative entropy and the distribution of the two logarithmic likelihood function ratio. Taking a stationary Gaussian process for example, this paper studies the discrete process of Tsallis entropy rate.It equal to Shannon entropy rate,when the parameter tends to1.At the end of the paper, we introduced the Shannon entropy and Tsallis entropy of continuous process by taking Brownian motion for example.By the K-L expansion of stochastic process,the paper comes to the conclusion that the Shannon entropy and the Tsallis entropy of Brownian motion is infinity.