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Distinguishing between cause and effect using time series observational data is a major challenge in many scientific fields. A new perspective has been provided based on the principle of Independence of Causal Mechanisms (ICM), leading to…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to…
What is the physical origin of the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of entropy as it appears in the statistical interpretation of the second law of thermodynamics. At the…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance…
We show that the Cerf-Adami inequalities do not necessarily depend on conditional entropies nor any reference to Markov chains. While the latter are not explicit in the original form, they are often implied in certain derivations. We also…
It is shown that quantum mechanics is, like thermodynamics, a phenomenological theory i.e., not a causal theory, ( not because it is a statistical theory - statistical theories with caused probability distributions can be regarded as…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we…
In any physical theory that admits true indeterminism, the thermodynamic arrow of time can arise regardless of the system's initial conditions. Hence on such theories time's arrow emerges out of the basic physical interactions. The example…
Quantum mechanics allows the occurrence of events without having any definite causal order. Here, it is shown that the application of two different thermal channels in the causally inseparable order can enhance the potential to extract…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
"Ceci n'est pas une pipe" wrote Ren\'e Magritte on what was only the representation of a pipe. Phenomena and their physical descriptions differ, and in particular the laws ruling the former might enjoy symmetries that have to be spent to…
We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the…
The notions of cause and effect are widely employed in science. I discuss why and how they are rooted into thermodynamics. The entropy gradient (i) explains in which sense interventions affect the future rather than the past, and (ii)…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…