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Entropy

Entropy

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...

Entropy

Entropy

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.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Calculating Standard Free Energy Changes

Calculating Standard Free Energy Changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...

Titration Calculations: Weak Acid - Strong Base

Titration Calculations: Weak Acid - Strong Base

Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:

Titration Calculations: Strong Acid - Strong Base

Titration Calculations: Strong Acid - Strong Base

Calculating pH for Titration Solutions: Strong Acid/Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:

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Updated: Jan 30, 2026

Optimization of Processing of Tiebangchui with Highland Barley Wine Based on the Box-Behnken Design Combined with the Entropy Method

Optimization of Processing of Tiebangchui with Highland Barley Wine Based on the Box-Behnken Design Combined with the Entropy Method

Published on: May 19, 2023

Ensemble-based topological entropy calculation (E-tec).

Eric Roberts¹, Suzanne Sindi¹, Spencer A Smith²

¹School of Natural Sciences, University of California, Merced, Merced, California 95343, USA.

Chaos (Woodbury, N.Y.)

|February 3, 2019

Summary

This summary is machine-generated.

We introduce Ensemble-based Topological Entropy Calculation (E-tec) to measure chaotic dynamics complexity. This method uses a "rubber band" around trajectories to efficiently compute a lower-bound for topological entropy in 2D systems.

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Area of Science:

Dynamical Systems
Computational Geometry
Fluid Dynamics

Background:

Topological entropy quantifies chaotic dynamics complexity by analyzing distinguishable orbits.
Existing methods for 2D systems often involve complex trajectory braiding analysis.

Purpose of the Study:

Introduce Ensemble-based Topological Entropy Calculation (E-tec) for a lower-bound estimation of topological entropy.
Develop a computationally efficient method for 2D dynamical systems.

Main Methods:

Utilize a "rubber band" (piece-wise linear curve) evolving with an ensemble of trajectories.
Employ computational geometry to track the rubber band's deformation by data points.
Leverage local updates based on trajectory configurations for efficiency.

Main Results:

E-tec provides a lower-bound for topological entropy based on the rubber band's exponential growth rate.
The method was validated on a chaotic lid-driven cavity flow.
Demonstrated convergence of E-tec's approximation with increasing ensemble size and trajectory duration.

Conclusions:

E-tec offers an efficient and validated approach to approximate topological entropy in 2D chaotic systems.
The method's computational efficiency stems from local updates of the evolving rubber band.
E-tec's accuracy improves with larger ensembles and longer trajectory observations.