Related papers: The Boltzmann distribution and the quantum-classic…
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…
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…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
Quantum computing raises the possibility of solving a variety of problems in physics that are presently intractable. A number of such problems involves the physics of systems in or near thermal equilibrium. There are two main ways to…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of the relativistic quantum mechanics, the…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
Quantum Boltzmann machines are natural quantum generalizations of Boltzmann machines that are expected to be more expressive than their classical counterparts, as evidenced both numerically for small systems and asymptotically under various…
The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find the…
A thermodynamic system of non-interacting quantum particles changes its statistical distribution formulas if there is a universal limitation for the size of energetic quantum leaps (magnitude of quantum leaps smaller than Planck energy). By…
To explore the thermal transport procedure driven by temperature gradient in terms of linear response theory, Luttinger et al. proposed the thermal scalar and vector potential[1,2] . In this manuscript, we try to address the microscopic…