相关论文: Does classical mechanics always adequately describ…

Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…

Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…

Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…

Out of thermal equilibrium, an environment imposes effective mechanical forces on microscopical nanofabricated devices, chemical or biological systems. Here we address the question of how to calculate these forces together with the response…

Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…

Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…

The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…

The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…

By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…

An axiomatic formalism for a minimal irreversible quantum mechanics is introduced. It is shown that a quantum equilibrium and the decoherence phenomenon are consequences of the axioms and that Lyapunov variables, exponential survival…

We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…

We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a…

We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…

This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…

In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…