Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here theoretical framework based on an optimal thermodynamic integration scheme, where the can be efficiently evaluated using regularizing paths. This avoids slowly convergent fluctuating contributions and leads low-variance...

Abstract It is widely believed that Hawking radiation originates from excitations near the horizons of black holes (Hawking in Commun Math Phys 43:199, 1975, Giddings Lett B 754:39, 2016, Mathur Class Quantum Gravity 26:224001, 2009). However, (Phys 2016) proposed spectrum characterizes evaporating semi-classical a quantum “atmosphere”, which extends beyond horizon hole. Although several resear...

The concept of Shannon entropy as a measure of disorder is introduced and the generalisations of the Rényi and Tsallis entropy are motivated and defined. A number of different estimators for Shannon, Rényi and Tsallis entropy are defined in the theoretical part and compared by simulation in the practical part. In this work the nearest neighbour estimator presented in Leonenko and Pronzato (2010...

This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

We introduce a generalized thermostatistics based on Kolmogorov-Nagumo averages and appropriately selected information measures. The formalism includes Tsallis non-extensive thermostatistics, but also extensive thermostatistics based on Rényi entropy. The Curie-Weiss model is discussed as an example.