Related papers: Statistical and strict momentum conservation
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…
We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
The non-conservation of entanglement, when two or more particles interact, sets it apart from other dynamical quantities like energy and momentum. It does not allow the interpretation of the subtle dynamics of entanglement as a flow of this…
Based on Newton's laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed oscillating universe. We find that the behaviour of the…
String theory predicts that the couplings of Nature descend from dynamical fields. All known string-motivated particle physics models also come with a wide range of possible extra sectors. It is common to posit that such moduli are frozen…
The momentum conservation sum rule for deep inelastic scattering (DIS) from composite particles is investigated using the general theory of relativity. For two 1+1 dimensional examples, it shown that covariant theories automatically satisy…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
If a macroscopic (random) classical system is put into a random state in phase space, it will of course the most likely have an almost maximal entropy according to second law of thermodynamics. We will show, however, the following theorem:…
We relate the breakdown of equations of states for the mechanical pressure of generic dry active systems to the lack of momentum conservation in such systems. We show how sources and sinks of momentum arise generically close to confining…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics…
We analyze the laws of conservation of momentum and angular momentum in classical electrodynamics of material media with bound charges, and explore the possibility to describe the properties of such media via a discrete set of point-like…
In a macroscopic (quantum or classical) Hamiltonian system, we prove the second law of thermodynamics in the forms of the minimum work principle and the law of entropy increase, under the assumption that the initial state is described by a…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
Using classical electrodynamics, this work analyzes the dynamics of a closed microwave cavity as a function of its center of energy. Starting from the principle of momentum conservation, expressions for the maximum electromagnetic momentum…
We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and…
The total angular momentum of a close system is a conserved quantity, which should remain constant in time for any excitation experiment once the pumping signal has extinguished. Such conservation, however, is never satisfied in practice in…