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It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
We firstly revisit the importance, naturalness and limitations of the so-called optical metrics for describing the propagation of light rays in the limit of geometric optics. We then exemplify their flexibility and nontriviality in some…
The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…
Special relativity (SR) with a privileged frame is a framework, which, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light but includes a privileged frame as an…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory…
Metric mean dimension is a dynamical counterpart of the box dimension in fractal geometry to characterize the topological complexity of infinite entropy systems. The classical variational principle states that topological entropy equals the…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
Metric-affine theories of gravity provide an interesting alternative to General Relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz…
Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a…
Quantum gravity is studied in a semiclassical approximation and it is found that to first order in the Planck length the effect of quantum gravity is to make the low energy effective spacetime metric energy dependent. The diffeomorphism…
In this letter we reflect on the propagation of gravitational waves in alternative theories of gravity, which are typically formulated using extra gravitational degrees of freedom in comparison to General Relativity. We propose to…
The bimetric variational principle is a subtle reinterpretation of general relativity that assumes the spacetime connection to be generated by an independent metric. Unlike the so called Palatini formalism that promotes the connection into…
This work is devoted to study the thermodynamic behavior of photon--like particles within the \textit{rainbow} gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…