Statistical Mechanics
Single-trajectory spectral analysis of scaled Brownian motion (1903.06673v1)
Vittoria Sposini, Ralf Metzler, Gleb Oshanin
2019-03-15
A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times,
. In many experimental situations one is able to garner only relatively few stochastic time series of finite
, such that practically neither an ensemble average nor the asymptotic limit
Efficient uniform generation of random derangements with the expected distribution of cycle lengths (1809.04571v3)
J. R. G. Mendonça
2018-09-12
We show how to generate random derangements with the expected distribution of cycle lengths by two different techniques: random restricted transpositions and sequential importance sampling. The algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Our data suggest that the mixing time (in the total variance distance) of the algorithm based on random restricted transpositions is
with
and
the size of the derangement. For the sequential importance sampling algorithm we prove that it generates random derangements in
time with a small probability
of failing.
Exact combinatorial approach to finite coagulating systems through recursive equations (1809.07239v3)
Michał Łepek, Paweł Kukliński, Agata Fronczak, Piotr Fronczak
2018-09-19
This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classic approach the mean-field Smoluchowski coagulation is used. However, the assumptions of the mean-field theory are rarely met in real systems which limits the accuracy of the solution. In our approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters and applying monodisperse initial conditions, the exact expression for the probability of finding a coagulating system with an arbitrary kernel in a given cluster configuration is derived. Then, the average number of such clusters and the standard deviation of these solutions can be calculated. In this work, recursive equations for all possible growth histories of clusters are introduced. The correctness of our expressions was proved based on the comparison with numerical results obtained for systems with constant, multiplicative and additive kernels. For the first time the exact solutions for the multiplicative and additive kernels were obtained with this framework. In addition, our results were compared with the results arising from the solutions to the mean-field Smoluchowski equation. Our theoretical predictions outperform the classic approach.
Entropy production in thermal phase separation: a kinetic-theory approach (1808.07698v3)
Yudong Zhang, Aiguo Xu, Guangcai Zhang, Yanbiao Gan, Zhihua Chen, Sauro Succi
2018-08-23
Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.
Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies (1808.01172v3)
Petr Jizba, Jan Korbel
2018-08-03
In this letter we show that the Shore--Johnson axioms for Maximum Entropy Principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof, we substantiate our point by analyzing the effect of weak correlations and discuss two pertinent examples:
-qubit quantum system and strongly interacting nuclear systems.
Don't forget to Follow and Resteem. @arxivsanity
Keeping everyone inform.