Related papers: Algorithmic independence of initial condition and …
In a previous paper [1] we considered the question, "What underlying property of nature is responsible for the second law?" A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second…
Given a list of $N$ states with probabilities $0<p_1\leq\cdots\leq p_N$, the average conditional algorithmic information $\bar I$ to specify one of these states obeys the inequality $H\leq\bar I<H+O(1)$, where $H=-\sum p_j\log_2p_j$ and…
We demonstrate that the algorithmic information content of a system is deeply connected to its potential dynamics, thus affording an avenue for moving systems in the information-theoretic space and controlling them in the phase space. To…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…
Recently, a thermodynamic definition of time has been introduced. This definition is useful to find approach some open problems in physics. But, it was obtained by a phenomenological approach and a logical inconsistency appears in the…
Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked…
It was recently shown \cite{opposite} that systems with opposite thermodynamic arrows of time could have moderate mutual interaction with neither destroying the order of the other. Such interaction includes signaling. Signals, however, may…
We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to…
The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…
In this paper we lay out an argument that generically the psychological arrow of time should align with the thermodynamic arrow of time where that arrow is well-defined. This argument applies to any physical system that can act as a memory,…
This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
We are not only observers but also actors of reality. Our capability to intervene and alter the course of some events in the space and time surrounding us is an essential component of how we build our model of the world. In this doctoral…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…