Related papers: Finite-State Classical Mechanics
We briefly show how classical mechanics can be rederived and better understood as a consequence of three assumptions: infinitesimal reducibility, deterministic and reversible evolution, and kinematic equivalence.
This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
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…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
Transmitting energy and information are two essential aspects of nature. Recent findings suggest they are closely related, while a quantitative equivalence between them is still unknown. This thus motivates us to ask: Can information…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…
We provide a derivation of quantum theory in which the existence of an energy observable that generates the reversible dynamics follows directly from information-theoretic principles. Our first principle is that every reversible dynamics is…
In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare, and, hence, quantifying possible quantum…
We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…