A Note on Burg’s Modified Entropy in Statistical Mechanics

Abstract

Burg's entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg's Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg's modified entropy is a better measure than the standard Burg's entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg's modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg's modified entropy is used instead of conventional Burg's entropy in a maximum entropy probability density (MEPD) function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

Time-frequency domain joint precoding based on the LSTM network and repetitive HSR channel

“…1. The Yule-Walker method and Burg method are utilized for these estimations, indicating a trend where β 1 tends toward zero [12]- [15]. Hence, in the context of HSR channel, the CSI for the current time sequence is predominantly influenced by the model error from previous time sequences, with the model error ϵ n being shaped by the time-frequency domain channel data from historical time sequences.…”