Related papers: The Boltzmann distribution and the quantum-classic…
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…
Open quantum systems play a central role in contemporary nanoscale technologies, including molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical…
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no…
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…
By contrasting the performance of two quantum annealers operating at different temperatures, we address recent questions related to the role of temperature in these devices and their function as `Boltzmann samplers'. Using a method to…
We study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric…
We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…
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…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles…
Using the linearized version of the time dependent Gross-Pitaevskii equation we calculate the dynamic response of a Bose-Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink---and even diverge---but they nevertheless balance to yield the Planck…
Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang1}. In this paper we examine the validity of this…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…