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Gibbs Free Energy

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...

Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

Equilibrium Conditions for a Particle

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

Free Energy and Equilibrium

Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔG is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
The reaction quotient, Q, is a convenient measure of the status of an...

Free Energy and Equilibrium

Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
Recall that Q is the numerical value of the mass action expression...

Reaction Mechanisms: The Steady-State Approximation

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The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...

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Updated: May 16, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Constructing the generalized Gibbs ensemble after a quantum quench.

Jean-Sébastien Caux¹, Robert M Konik

¹Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, The Netherlands.

Physical Review Letters

|December 11, 2012

Summary

This summary is machine-generated.

We studied the dynamics of a 1D Bose gas after release from a trap. Our numerical renormalization group method tracks long-time behavior and compares it to the generalized Gibbs ensemble predictions.

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

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Last Updated: May 16, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

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

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Published on: December 4, 2017

Area of Science:

Quantum physics
Many-body systems
Statistical mechanics

Background:

The Lieb-Liniger model describes one-dimensional Bose gases.
Understanding out-of-equilibrium dynamics in quantum systems is a key challenge.
The generalized Gibbs ensemble is a proposed framework for describing such dynamics.

Purpose of the Study:

To investigate the out-of-equilibrium dynamics of a 1D Bose gas released from a parabolic trap.
To develop and apply a numerical renormalization group method for tracking dynamics to infinite time.
To compare the observed long-time dynamics with predictions from the generalized Gibbs ensemble.

Main Methods:

Utilizing a numerical renormalization group (NRG) approach.
Leveraging an underlying exactly solvable nonrelativistic theory.
Tracking the post-quench dynamics of the Bose gas to infinite time.

Main Results:

The study successfully tracked the out-of-equilibrium dynamics of the 1D Bose gas to infinite time.
A general construction of the generalized Gibbs ensemble for integrable models was established.
A comparison between the NRG method's long-time dynamics and generalized Gibbs ensemble predictions was performed.

Conclusions:

The numerical renormalization group method provides a powerful tool for studying quantum gas dynamics.
The generalized Gibbs ensemble offers a valuable theoretical framework for understanding equilibration in integrable systems.
The study validates and refines our understanding of quantum gas behavior after a quench.