ﻻ يوجد ملخص باللغة العربية
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this Letter, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focussing on a particular member of this family -- the co-emission divergence rate -- we show that it can be computed efficiently, behaves qualitatively similar to other commonly-used measures in their regimes of applicability, and remains well-behaved in scenarios where other measures break down.
In recent letter [Phys. Rev. Lett {bf 121}, 070601 (2018), arXiv:1802.06554], the speed limit for classical stochastic Markov processes is considered, and a trade-off inequality between the speed of the state transformation and the entropy production
A quantum ensemble ${(p_x, rho_x)}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a stochastic quantum c
Estimating the expected value of an observable appearing in a non-equilibrium stochastic process usually involves sampling. If the observables variance is high, many samples are required. In contrast, we show that performing the same task without sam
We investigate the standard deviation $delta v(tsamp)$ of the variance $v[xbf]$ of time series $xbf$ measured over a finite sampling time $tsamp$ focusing on non-ergodic systems where independent configurations $c$ get trapped in meta-basins of a gen
We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the