Related papers: Towards Boltzmann Distribution
Based on a cocycle structure, we identify a new derivation of the Boltzmann distribution for finite energy-level systems from the maximal entropy principle (MEP). Our approach does not rely on the method of the Lagrange multiplier, and it…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
We investigate the properties of a Kolmogorov equation governing the time evolution of the probability distribution defined in phase space. Energy is strictly conserved along a trajectory in phase space, meaning the equation is appropriate…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis,…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption. To tackle this issue, routing must…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a…
The sampling of Boltzmann distributions by stochastic Markov processes, can be strongly limited by the crossing time of high (free) energy barriers. As a result, the system may stay trapped in metastable states, and the relaxation time to…
The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…
A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
This paper is devoted to the study of the dynamics of charged particles in a weakly inhomogeneous dilute gas. More precisely, we consider the existence of unique global in time classical solutions for the Vlasov-MaxwellBoltzmann system and…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
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…