Related papers: Permutation entropy revisited
Along recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy…
This paper studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is…
We revisit textbook claims that entropy must increase and show that, under time-reversal invariant microscopic dynamics, no universal trajectory-wise or statistical assertion that the coarse-grained entropy $S(t)$ is non-decreasing can…
We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. We argue that an appropriate spacetime region associated with an observer from tI to t_P is the causal diamond…
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…
The entropy production rate (EPR), a key measure of thermodynamic irreversibility in stochastic thermodynamics, is difficult to determine directly in experiments, motivating lower-bound-based estimation from observations. However, a…
We define entanglement entropy in string perturbation theory using the orbifold method -- a stringy analog of the replica method in field theory. To this end, we use the Newton series to analytically continue in $N$ the partition functions…
We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the…
Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
Many learning problems require uncovering a hidden ordering that reveals structure in unordered data, such as monotonicity in sorting or spatial continuity in jigsaw reconstruction. In these settings, permutations can be learned as latent…
In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for…
Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse…
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental sciences since several decades. Time series of water and matter fluxes and nutrient concentrations from these…