Related papers: Algorithmic independence of initial condition and …

The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…

The direct and indirect experimental proofs of a strong time invariance violation in optics are discussed. Time noninvariance for present day becomes the only real physical base for explanation the origin of the most phenomena in nonlinear…

In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…

Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…

We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling…

People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…

The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…

Completely positive trace preserving maps are essential for the formulation of the second law of thermodynamics. The dynamics of quantum systems, correlated with their environments, are in general not described by such maps. We explore how…

We demonstrate that irreversibility arises from the principle of microscopic reversibility and the presence of memory in the time evolution of a single copy of a system driven by a protocol. We introduce microscopic reversibility by using…

Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…

Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the…

This paper provides a concise description of the free energy principle, starting from a formulation of random dynamical systems in terms of a Langevin equation and ending with a Bayesian mechanics that can be read as a physics of sentience.…

Information Geometric Causal Inference (IGCI) is a new approach to distinguish between cause and effect for two variables. It is based on an independence assumption between input distribution and causal mechanism that can be phrased in…

Why is it that a ticking clock typically becomes less accurate when subject to outside noise but rarely the reverse? Here, we formalize this phenomenon by introducing process causal asymmetry - a fundamental difference in the amount of past…

The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…

The estimator of a causal directed acyclic graph (DAG) with the PC algorithm is known to be consistent based on independent and identically distributed samples. In this paper, we consider the scenario when the multivariate samples are…

Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an…

The dynamics of free vibrations of a chain of atoms is investigated taking into account the retardation of interactions. It is shown that all oscillations of the circuit are damped. The dynamics of forced vibrations of this chain of atoms…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…