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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.
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Entropy and the Second Law of Thermodynamics

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The Second Law of Thermodynamics

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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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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...

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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

Entropy and irreversibility in dynamical systems.

Oliver Penrose¹

¹Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Colin Maclaurin Building, Heriot-Watt University, , Riccarton, Edinburgh EH14 4AS, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|November 20, 2013

Summary

This summary is machine-generated.

This study introduces a new way to define non-equilibrium entropy for chaotic systems, avoiding macroscopic states. It shows that even simple chaotic systems can exhibit irreversible behavior and significant entropy increases.

Keywords:

Arnold map Boltzmann’s principle chaotic dynamical system entropy irreversibility macrostates

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Area of Science:

Statistical Mechanics
Chaos Theory
Dynamical Systems

Background:

Traditional entropy definitions rely on macroscopic states (Boltzmann's principle S = klog W).
Understanding non-equilibrium entropy in chaotic systems is crucial for statistical mechanics.
Chaotic systems exhibit sensitive dependence on initial conditions, complicating entropy calculations.

Purpose of the Study:

To propose a novel method for defining non-equilibrium entropy in chaotic dynamical systems.
To demonstrate this method using a specific chaotic system example.
To explore the possibility of irreversible behavior and entropy increase in low-degree-of-freedom chaotic systems.

Main Methods:

Developed a new theoretical framework for non-equilibrium entropy that bypasses the need for macroscopic states.
Applied the proposed method to Arnold's 'cat' map, a well-known two-dimensional chaotic system.
Analyzed the system's behavior to quantify entropy changes.

Main Results:

The proposed method successfully defines non-equilibrium entropy without invoking macroscopic states.
Arnold's 'cat' map exhibits irreversible behavior consistent with a large increase in entropy.
This entropy increase occurs in a chaotic system with only two degrees of freedom.

Conclusions:

A new, macroscopic-state-independent definition of non-equilibrium entropy is feasible for chaotic systems.
Irreversible behavior and significant entropy production are possible even in simple, low-dimensional chaotic systems.
This work offers a new perspective on entropy in the context of chaos theory and statistical mechanics.