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Entropy Change in Reversible Processes

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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.
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Entropy Changes Accompanying Specific Processes

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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...

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Extensive chaos in the Lorenz-96 model.

A Karimi¹, M R Paul

¹Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.

Chaos (Woodbury, N.Y.)

|January 5, 2011

Summary

We analyzed the Lorenz-96 model

Area of Science:

Complex systems
Atmospheric dynamics
Chaos theory

Background:

The Lorenz-96 model simulates spatially extended chaotic systems like the atmosphere.
Understanding chaotic dynamics is crucial for weather forecasting.

Purpose of the Study:

Investigate how fractal dimension changes with system parameters in the Lorenz-96 model.
Explore spatiotemporal chaos and strong driving limits.

Main Methods:

Computed fractal dimension variations with system size and external forcing.
Analyzed transitions between periodic and chaotic dynamics.
Quantified deviations from extensivity in chaotic degrees of freedom.

Main Results:

Found alternating periodic and chaotic dynamics with increasing system size for low forcing.

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Observed chaotic dynamics for all system sizes past a critical forcing value.

Fractal dimension deviations from extensivity decreased non-monotonically with system size.

Conclusions:

Deviations from extensivity are linked to the addition of chaotic degrees of freedom.
Each deviation wavelength contains approximately two chaotic degrees of freedom.
Dimension density increases with forcing, indicating smaller chaotic degrees of freedom.