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Entropy

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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.
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Entropy

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Related Experiment Video

Updated: Jun 18, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Boolean chaos.

Rui Zhang¹, Hugo L D de S Cavalcante, Zheng Gao

¹Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA. rz10@phy.duke.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

Researchers discovered deterministic chaos in electronic logic gates without clock signals, creating ultrawideband signals up to 2 GHz. This electronic Boolean chaos could be used for ultrawideband radio wave generation.

Related Experiment Videos

Last Updated: Jun 18, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Area of Science:

Nonlinear dynamics
Electronic circuits
Chaos theory

Background:

Deterministic chaos is a complex behavior observed in nonlinear systems.
Electronic logic gates are fundamental components in digital systems.
Clocking signals are typically used to synchronize operations in digital circuits.

Purpose of the Study:

To investigate the emergence of deterministic chaos in a simple network of electronic logic gates operating without a clock signal.
To characterize the power spectrum of the chaotic signals generated.
To develop a model that can qualitatively reproduce the observed chaotic behavior.

Main Methods:

Experimental observation of signal behavior in an asynchronous electronic logic gate network.
Analysis of the power spectrum of the generated signals.
Development and simulation of an autonomously updating Boolean model incorporating history-dependent propagation times and pulse filtering.

Main Results:

Deterministic chaos was observed in the asynchronous electronic logic gate network.
The resulting power spectrum was ultrawideband, extending from DC to over 2 GHz.
The Boolean model qualitatively reproduced the experimental observations, including the effects of signal history and pulse filtering.

Conclusions:

Asynchronous electronic logic gate networks can exhibit deterministic chaos.
This phenomenon generates ultrawideband signals with potential applications.
Electronic Boolean chaos offers a novel approach for ultrawideband radio wave generation.