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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.

The Second Law of Thermodynamics

The Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be put...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

State Function, Exact and Inexact Differentials

State Function, Exact and Inexact Differentials

A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...

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Related Experiment Video

Updated: May 26, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Effective stochastic behavior in dynamical systems with incomplete information.

Michael A Buice¹, Carson C Chow

¹Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, Maryland 20892, USA.

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

|December 21, 2011

Summary

This summary is machine-generated.

We developed a new method to create effective stochastic equations for complex deterministic systems with incomplete information. This approach simplifies analysis and simulation of such systems, like coupled oscillators.

Related Experiment Videos

Last Updated: May 26, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Complex Systems Dynamics
Statistical Physics
Computational Modeling

Background:

Complex systems are often analytically intractable and computationally demanding to simulate.
Many real-world systems involve deterministic dynamics with partially unspecified configurations.
Understanding emergent behavior in such systems requires robust analytical and simulation tools.

Purpose of the Study:

To introduce a novel method for deriving effective stochastic equations from high-dimensional deterministic dynamical systems.
To handle systems where parts of the configuration are not precisely known.
To provide a framework applicable to various complex systems, including the Kuramoto model.

Main Methods:

Utilizing a response function path integral to construct an equivalent stochastic distribution.
Deriving the stochastic dynamics from the distribution of incomplete information.
Applying the method to the Kuramoto model of coupled oscillators.

Main Results:

An effective stochastic equation was derived for a single oscillator interacting with a bath of oscillators within the Kuramoto model.
The method successfully bridges deterministic dynamics with incomplete information to stochastic descriptions.
The procedure for applying this method to other complex systems was outlined.

Conclusions:

The developed method offers a powerful tool for analyzing and simulating complex deterministic systems with partial information.
This approach simplifies the study of systems that are otherwise analytically intractable.
The technique provides a pathway to understanding emergent phenomena in diverse scientific domains.