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Cyclic Processes And Isolated Systems

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...

Entropy Change in Reversible Processes

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.

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.

Second Order systems I

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...

Typical Model Studies

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.

Thermodynamic Systems

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of tea boiling in a kettle. The...

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Related Experiment Video

Updated: Jul 19, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Dynamical independence: Discovering emergent macroscopic processes in complex dynamical systems.

L Barnett¹, A K Seth^1,2

¹Sussex Centre for Consciousness Science, Department of Informatics, University of Sussex, Falmer, Brighton BN1 9QJ, United Kingdom.

Physical Review. E

|August 16, 2023

Summary

This summary is machine-generated.

We introduce a new method to identify emergent phenomena in complex systems. This approach quantifies dynamical independence to discover macroscopic variables with distinct behaviors, aiding in understanding multiscale systems.

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Last Updated: Jul 19, 2025

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Area of Science:

Complex Systems Science
Dynamical Systems Theory
Information Theory

Background:

Macroscopic phenomena often arise from complex, multivariate microscopic dynamics.
Understanding emergence requires distinguishing macroscopic behaviors from underlying microscopic processes.

Purpose of the Study:

To introduce a quantitative framework for emergence based on dynamical independence.
To develop methods for discovering emergent macroscopic variables in complex systems.
To enable the creation of multiscale emergence portraits.

Main Methods:

Defining emergence via dynamical independence of macroscopic variables.
Utilizing a Shannon information-based measure for dynamical dependence.
Developing explicit computations for linear systems (time and frequency domains).
Outlining applications to neurophysiological time-series data.

Main Results:

Quantification of dynamical dependence provides a measure of emergence.
The framework facilitates data-driven discovery of emergent phenomena.
Linear system analysis allows for explicit computation of dynamical dependence.
Emergence portraits can be inferred for complex systems, including neural systems.

Conclusions:

Dynamical independence offers a rigorous definition of emergence.
The proposed methods enable the identification and characterization of emergent behaviors.
This work provides a pathway for analyzing emergence across spatiotemporal scales in diverse systems.