Related papers: Probabilities and Path-Integral Realization of Exc…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…
We propose a misanthrope process, defined on a ring, which realizes the totally asymmetric simple exclusion process with open boundaries. In the misanthrope process, particles have no exclusion interactions in contrast to those in the…
This work deals with the physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential in the context of…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach…
The propagator and corresponding path integral for a system of identical particles obeying parastatistics are derived. It is found that the statistical weights of topological sectors of the path integral for parafermions and parabosons are…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
By using a fonctionelle of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general method. The essential equivalence between the MaxEnt process of the most…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the…
Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the data sources available. This paper shows how partial…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…
We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of…
If the generalized statistics suggested by Tsallis are used in statistical mechanics, the fluctuation-dissipation theorem no longer holds. Only in the limiting case where Boltzmann statistics are recovered is the theorem applicable. In…