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Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field plus pairing model in the strong pairing…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation…
This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
The influence of a curved spacetime $M$ on the physical behavior of an ideal gas of $N$ particles is analyzed by considering the phase space of the system as a region of the cotangent bundle $T^{*}M^{N}$ and using Souriau's Lie group…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference and velocity gradient are derived. No closure assumptions…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes…
In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type…
We consider a homogeneous plasma composed of $N$ particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the…
Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…