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Related Concept Videos

Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Causality in Epidemiology01:21

Causality in Epidemiology

Causality or causation is a fundamental concept in epidemiology, vital for understanding the relationships between various factors and health outcomes. Despite its importance, there's no single, universally accepted definition of causality within the discipline. Drawing from a systematic review, causality in epidemiology encompasses several definitions, including production, necessary and sufficient, sufficient-component, counterfactual, and probabilistic models. Each has its strengths and...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

Updated: May 11, 2026

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies
05:59

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies

Published on: October 6, 2023

Spurious causalities with transfer entropy.

Dmitry A Smirnov1

  • 1Saratov Branch of V. A. Kotel'nikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, 38 Zelyonaya St., Saratov 410019, Russia. smirnovda@yandex.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

Transfer entropy (TE) can falsely indicate bidirectional coupling in complex systems. Imperfect observations, like unobserved variables or low temporal resolution, can cause spurious causal influences.

Related Experiment Videos

Last Updated: May 11, 2026

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies
05:59

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies

Published on: October 6, 2023

Area of Science:

  • Complex systems analysis
  • Information theory
  • Causal inference

Background:

  • Transfer entropy (TE) is a key metric for inferring causal relationships in complex systems from time series data.
  • Bidirectional coupling is often inferred from non-zero TE values in both directions between two systems.
  • Existing interpretations may overlook conditions leading to false positives.

Purpose of the Study:

  • To investigate the phenomenon of "spurious couplings" in transfer entropy calculations.
  • To identify factors contributing to the misinterpretation of causal influences.
  • To analyze conditions under which spurious TE values can be significant.

Main Methods:

  • Exact computation of Transfer Entropy (TE) values for benchmark systems.
  • Analysis of imperfect observations, including unobserved variables, low temporal resolution, and observation errors.
  • Theoretical examination of conditions leading to large spurious TE.

Main Results:

  • Demonstration that non-zero TE in both directions does not exclusively imply bidirectional coupling.
  • Identification of imperfect observations as a general cause for spurious causal detection.
  • Quantification of conditions where spurious TE can exceed true causal influence.

Conclusions:

  • Transfer entropy analysis requires careful consideration of observation quality to avoid false causal inference.
  • Imperfect observations are a critical factor leading to spurious bidirectional coupling detection.
  • Understanding these limitations is crucial for accurate causal inference in complex systems.