Related papers: Classical Reciprocity Laws
Methods of statistical physics have proven valuable for studying the evolution of cooperation in social dilemma games. However, recent empirical research shows that cooperative behavior in social dilemmas is only one kind of a more general…
We prove that the Arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a…
We prove non-commutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws claim the splittings of some central extensions of globally constructed groups over some subgroups constructed by points…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
The Kepler's third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical…
The emergence of structure in cooperative relation is studied in a game theoretical model. It is proved that specific types of reciprocity norm lead individuals to split into two groups. The condition for the evolutionary stability of the…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Most of the logical objections against the classical laws of motion, as they are usually presented in textbooks, centre on the fact that defining force in terms of mass and acceleration, the first two laws are mere assertions of concepts to…
We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form $v(r)=g/r^\gamma$, with$\gamma\textgreater{}0$, for repulsive ($g\textgreater{}0$) and attractive ($g\textless{}0$)interactions. We…
Inspired by Wannier's threshold law, we recognize that collision complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the…
The purpose of this paper is two-fold. First, to make clear (and de-mystify) the basic concepts of classical thermodynamics, and thus to enable the integration of thermodynamics within systems modeling and control. Second, to demonstrate…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
What if gravity is classical? If true, a consistent co-existence of classical gravity and quantum matter requires that gravity exhibit irreducible fluctuations. These fluctuations can mediate classical correlations, but not quantum…
We provide the classical mechanics of many particles moving in canonically twist-deformed space-time. In particular, we consider two examples of such noncommutative systems - the set of N particles moving in gravitational field as well as…
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
People often engage in costly cooperation, especially in repeated interactions. When deciding whether to cooperate, individuals typically take into account how others have acted in the past. For instance, when one person is deciding whether…
This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…