Statistical Energy Analysis is a statistical method in vibroacoustics entirely based on the application of energy balance that is the first principle of thermodynamics. In this study, the definition of vibrational entropy is introduced for sub-systems containing energy and modes. The rate of entropy production at interfaces between sub-systems is also derived. Finally, in steady-state condition...

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p < d/(d − 1) and p > d/(d − 1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of ...

Let KpX1, . . . , Xnq and HpXn|Xn ́1, . . . , X1q denote the Kolmogorov complexity and Shannon’s entropy rate of a stationary and ergodic process tXiui“ ́8. It has been proved that KpX1, . . . , Xnq n ́HpXn|Xn ́1, . . . , X1q Ñ 0, almost surely. This paper studies the convergence rate of this asymptotic result. In particular, we show that if the process satisfies certain mixing conditions, then the...

We generalize Gaspard's method for computing the ε-entropy production rate in Hamiltonian systems to dissipative systems with attractors considered earlier by Tél, Vollmer, and Breymann. This approach leads to a natural definition of a coarse grained Gibbs entropy which is extensive, and which can be expressed in terms of the SRB measures and volumes of the coarse graining sets which cover the ...

In this work, we extend a variable-length source coding theorem for discrete memoryless sources to ergodic time-invariant Markov sources of arbitrary order. To accomplish this extension, we establish a formula for the R enyi entropy rate lim n!1 H (n)=n. The main tool used to obtain the R enyi entropy rate result is Perron-Frobenius theory. We also examine the expression of the R enyi entropy r...

We present here two methods of entropy coding for the lattice codevectors. We compare our entropy coding methods with one method previously presented in the literature from the point of view of rate-distortion as well as of the computation complexity and memory requirements. The results are presented for artificial Laplacian and Gaussian data, as well as for LSF parameters of speech signals. In...

We demonstrate an efficient formula to compute the entropy rate H(μ) of a hidden Markov process with q output symbols where at least one symbol is unambiguously received. Using an approximation to H(μ) to the first N terms we give a O(Nq) algorithm to compute the entropy rate of the hidden Markov model. We use the algorithm to estimate the entropy rate when the parameters of the hidden Markov m...