Related papers: Entropy from Machine Learning
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
Entanglement measures such as the entanglement entropy have become an indispensable tool to identify the fundamental character of ground states of interacting quantum many-body systems. For systems of interacting spin or bosonic degrees of…
The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
Inferring a generative model from data is a fundamental problem in machine learning. It is well-known that the Ising model is the maximum entropy model for binary variables which reproduces the sample mean and pairwise correlations.…
We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is…
We consider a generic classical many particle system described by an autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket $\{H,V \}$…
An efficient approach of measuring the absolute free energy in parallel tempering Monte Carlo using the exponential averaging method is discussed and the results are compared with those of population annealing Monte Carlo using the…
We propose a free-energy-perturbation approach accelerated by machine-learning potentials to efficiently compute transition temperatures and entropies for all rungs of Jacob's ladder. We apply the approach to the dynamically stabilized…
Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is…
Transferring knowledge from one neural network to another has been shown to be helpful for learning tasks with few training examples. Prevailing fine-tuning methods could potentially contaminate pre-trained features by comparably high…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
We present a numerical analysis of the entropy rate and statistical complexity related to the spin flip dynamics of the 2D Ising Ferromagnet at different temperatures T. We follow an information theoretic approach and test three different…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
Metric learning aims at learning a distance which is consistent with the semantic meaning of the samples. The problem is generally solved by learning an embedding for each sample such that the embeddings of samples of the same category are…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…