Related papers: Statistical Representation of Spacetime
The notion of inflation (past or present) in standard cosmological models is shown to be a consequence of a sufficiently high second law entropy production from the internal heating of the universal expansion. The longitudinal viscous…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
A change in a stochastic system has three representations: Probabilistic, statistical, and informational: (i) is based on random variable $u(\omega)\to\tilde{u}(\omega)$; this induces (ii) the probability distributions $F_u(x)\to…
We experimentally study cosmological particle production in a two-dimensional Bose-Einstein condensate, whose density excitations map to an analog cosmology. The expansion of spacetime is realized with tunable interactions. The particle…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS = dQ/T hold for all local acceleration horizons through each spacetime point, where dS is one quarter the horizon area…
Motivated by the corrected form of the entropy-area law, and with the help of von Neumann entropy of quantum matter, we construct an emergent spacetime by the virtue of the geometric language of statistical information manifolds. We discuss…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Here…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
In the present mainstream cosmology, matter and spacetime emerged from a singularity and evolved through four distinct periods: early inflation, radiation, dark matter and late-time inflation (driven by dark energy). During the radiation…
In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one of the variables, there exists a particular distribution of states of the second variable.…
When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…
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…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…