Related papers: Information dynamics and the arrow of time
Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has…
The mechanism by which thermodynamics sets the direction of time's arrow has long fascinated scientists. Here, we show that a machine learning algorithm can learn to discern the direction of time's arrow when provided with a system's…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
We study probabilistic cellular automata (PCA) and quantum cellular automata (QCA) as frameworks for solving the Maximum Independent Set (MIS) problem. We first introduce a synchronous PCA whose dynamics drives the system toward the…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, $w_{\rm irr}$, and irreversible entropy production, $\Delta_i s$, within the stochastic energetics framework. Restating the second law of…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
The purpose of this paper is to explain a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vector-valued, second-order stochastic…
For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are…
The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time…
This paper is a continuation of the paper gr-qc/0203045 and is devoted to the problem of the arrow of time. A deterministic past-directed dynamics is constructed, which results in the retrodictive universe. A future-directed dynamics of the…