Related papers: Understanding causation via correlations and linea…
A general non-linear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. This allows us to obtain a greatly generalized Kubo type formula. Applied to a mesoscopic system…
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…
Fluctuations in conjugate thermodynamic variables are studied using the cross-correlation function. A new procedure is given enabling the derivation of fluctuation formulas for a system in equilibrium. Specifically, the cross-correlation…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
Causality defines the relationship between cause and effect. In multivariate time series field, this notion allows to characterize the links between several time series considering temporal lags. These phenomena are particularly important…
We discuss fluctuation-dissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to non-equilibrium can…
Recently, it has been shown that the causality and information flow between two time series can be inferred in a rigorous and quantitative sense, and, besides, the resulting causality can be normalized. A corollary that follows is, in the…
I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical…
The constraints arising for a general set of causal relations, both classically and quantumly, are still poorly understood. As a step in exploring this question, we consider a coherently controlled superposition of "direct-cause" and…
The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among other applications. Here, a mathematically…
We introduce a novel framework for causal explanations of stochastic, sequential decision-making systems built on the well-studied structural causal model paradigm for causal reasoning. This single framework can identify multiple,…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
Discussions on causal relations in real life often consider variables for which the definition of causality is unclear since the notion of interventions on the respective variables is obscure. Asking 'what qualifies an action for being an…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However a widely accepted formal definition of causal influence between observables is still missing. In the framework of…
Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now…
The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear…
Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of…