Related papers: The Boltzmann distribution and the quantum-classic…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to understand phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing…
A quantum linear Boltzmann equation is proposed, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with. Due to this operator structure it is a non-Abelian linear…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
In this paper, we address the problem how to represent a classical data distribution in a quantum system. The proposed method is to learn quantum Hamiltonian that is such that its ground state approximates the given classical distribution.…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
Classical-like formulas are given in order to evaluate thermal averages of observables belonging to a quantum nonlinear system with dissipation described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys. (N.Y.) 149,…
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
The Boltzmann distribution predicts the collective behavior of systems at thermodynamic equilibrium as a function of their constituent parts. Yet most systems in nature are not at equilibrium, and a unified theory of their behavior does not…
Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We re-consider the old problem of Brownian motion in homogeneous high-temperature thermal environment. The semiclassical theory implies that the diffusion coefficient does not depend on whether the thermal fluctuations are correlated in…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
We consider one-dimensional, integrable many-body classical and quantum systems in thermal equilibrium. In the classical case, we use the classical limit of the Bethe equations to obtain a self-consistent integral equation whose solution…
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…
Using a generalized Langevin equation of motion, quantum ballistic thermal transport is obtained from classical molecular dynamics. This is possible because the heat baths are represented by random noises obeying quantum Bose-Einstein…