Related papers: Towards Boltzmann Distribution
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
We demonstrate that the most probable state of a conserved system with a limited number of entities or molecules is the state where non-Gaussian and non-chi-square distributions govern. We have conducted a thought experiment using a…
Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
Using the principle of detailed balance and the assumption on the absorption cross-section consistent with available astrophysical data, we obtain the energy distribution of atoms in the field of thermal blackbody radiation and show that…
For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
The origin of the Boltzmann factor is revisited. An alternative derivation from the microcanonical picture is given. The Maxwellian distribution in a mono-dimensional ideal gas is obtained by following this insight. Other possible…
We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
Within the framework of the post-Newtonian $2\frac12$ approximation theory, a kinetic theory for relativistic gases in the presence of gravitational fields is developed. The Boltzmann equation and the equilibrium Maxwell-J\"uttner…
Selected aspects of the Maxwell-Boltzmann for molecular speeds are discussed, with special attention to physical effects of the low speed and high speed limits. We use simple approaches to study several topics which could be included in…
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…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…