Related Experiment Video
Updated: Nov 27, 2025
11:15
Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
34.1K
Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach
Carlos Islas1, Pablo Padilla2, Marco Antonio Prado1,2
1Universidad Autónoma de la Ciudad de México, Doctor García Diego núm. 168, Cuauhtémoc, Ciudad de México 06720, Mexico.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study proposes brain information processing follows optimal transport of Shannon entropy. This leads to a Monge-Ampère type equation for neuronal information flow.
Area of Science:
- Neuroscience
- Information Theory
- Mathematical Physics
Background:
- Brain activity analysis often employs information theory.
- Understanding information processing in neural networks is crucial.
- Optimal transport theory provides a framework for analyzing distributions.
Purpose of the Study:
- To investigate brain activity through an information theoretic lens.
- To explore the optimality of Shannon entropy transport in the brain.
- To derive a mathematical model for neuronal information flow.
Main Methods:
- Utilizing the Monge-Kantorovich framework for optimal transport.
- Applying information theory to analyze brain activity.
- Deriving a Monge-Ampère type equation for information flow.
Main Results:
- Proposed that certain brain processes satisfy an optimal transport of informational entropy condition.
- Derived a Monge-Ampère type equation for information flow, accounting for neuronal branching.
- Discussed a version of Murray's law within this framework.
Conclusions:
- Brain information processing can be modeled using optimal transport of entropy.
- The derived equation offers insights into neuronal information flow dynamics.
- This approach provides a novel perspective on neural computation and structure-function relationships.
Keywords:
Monge–Ampère equationMurray’s lawinformational entropyneuronal branching structuresneuroscienceoptimal transportvariational calculusMore Related Videos
Related Concept Videos
01:22Entropy within the Cell
12.3K
A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
12.3K
01:20Parallel Processing
450
The brain processes sensory information rapidly due to parallel processing, which involves sending data across multiple neural pathways at the same time. This method allows the brain to manage various sensory qualities, such as shapes, colors, movements, and locations, all concurrently. For instance, when observing a forest landscape, the brain simultaneously processes the movement of leaves, the shapes of trees, the depth between them, and the various shades of green. This enables a quick and...
450
01:18Entropy
3.2K
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...
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...
3.2K
02:39Entropy
33.6K
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...
33.6K
01:10Entropy Change in Reversible Processes
3.0K
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 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.
3.0K
01:01Neuroplasticity
1.2K
Neuroplasticity reflects the brain's remarkable capacity to adapt and evolve, responding dynamically to learning, experiences, or injury by reorganizing its neural circuitry. This reorganization involves creating new neural connections and refining old ones through a series of biological processes that contribute to the brain's lifelong development and adaptability.
1.2K