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Occupation Times on the Legs of a Diffusion Spider.
Entropy (Basel)
February 2025
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada.
We study the joint moments of occupation times on the legs of a diffusion spider. Specifically, we give a recursive formula for the Laplace transform of the joint moments, which extends earlier results for a one-dimensional diffusion. For a Bessel spider, of which the Brownian spider is a special case, our approach yields an explicit formula for the joint moments of the occupation times.
View Article and Find Full Text PDFNeural network representations of multiphase Equations of State.
Sci Rep
December 2024
Los Alamos National Laboratory, Los Alamos, NM, USA.
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency.
View Article and Find Full Text PDFA new extension of XLindley distribution with mathematical properties, estimation, and application on the rainfall data.
Heliyon
October 2024
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh, 11587, Saudi Arabia.
Data analysis is indeed quite popular and crucial in various fields such as meteorology, hydrology, epidemiology, economics, and biology. So, the purpose of this study is to introduce a new probability distribution to analyze rainfall data. A new extension of XLindley distribution is introduced using the alpha power transformation technique.
View Article and Find Full Text PDFGeneralized Linear Response Theory for the Full Quantum Work Statistics.
Phys Rev Lett
August 2024
Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study nonequilibrium fluctuations in complex quantum systems.
View Article and Find Full Text PDFIntegral fluctuation theorems and trace-preserving map.
Phys Rev E
June 2024
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China.
The detailed fluctuation theorem implies symmetry in the generating function of entropy production probability. The integral fluctuation theorem directly follows from this symmetry and the normalization of the probability. In this paper, we rewrite the generating function by integrating measurements and evolution into a constructed mapping.
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