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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...

An Introduction to Free Energy

An Introduction to Free Energy

How can we compare the energy that releases from one reaction to that of another reaction? We use a measurement of free energy to quantitate these energy transfers. Scientists call this free energy Gibbs free energy (abbreviated with the letter G) after Josiah Willard Gibbs, the scientist who developed the measurement. According to the second law of thermodynamics, all energy transfers involve losing some energy in an unusable form such as heat, resulting in entropy. Gibbs free energy...

Gibbs Free Energy and Thermodynamic Favorability

Gibbs Free Energy and Thermodynamic Favorability

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

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...

Potential-Energy Criterion for Equilibrium

Potential-Energy Criterion for Equilibrium

Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to...

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Related Experiment Video

Updated: Jun 12, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Forced Friends: Why the Free Energy Principle Is Not the New Hamilton's Principle.

Bartosz Michał Radomski¹, Krzysztof Dołęga²

¹Institute for Philosophy II, Ruhr-Universität Bochum, D-44780 Bochum, Germany.

Entropy (Basel, Switzerland)

|September 27, 2024

Summary

The free energy principle is analogous, not equivalent, to Hamilton's principle of stationary action in statistical mechanics. This clarification resolves ambiguity in scientific literature regarding their relationship.

Keywords:

Hamilton’s principle analogy equivalence formal analogy free energy principle philosophy of science similarity

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Last Updated: Jun 12, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Area of Science:

Statistical Mechanics
Theoretical Physics
Computational Neuroscience

Background:

The relationship between the free energy principle and Hamilton's principle of stationary action is frequently asserted but poorly defined in scientific literature.
Existing literature presents conflicting views, suggesting the free energy principle is similar, analogous, equivalent, or a version of Hamilton's principle.

Purpose of the Study:

To rigorously investigate and clarify the precise nature of the relationship between the free energy principle and Hamilton's principle.
To examine the two most plausible interpretations of the claimed relationship: a strong (equivalence) and a weak (analogy) interpretation.

Main Methods:

Analysis of the strong interpretation: assessing the implications of equating the free energy principle with Hamilton's principle.
Analysis of the weak interpretation: evaluating the structural similarities and analogies between the two principles.
Logical deduction and theoretical comparison of the principles within the framework of statistical mechanics.

Main Results:

The strong interpretation leads to an untenable dilemma for proponents of the free energy principle, suggesting equivalence is not a valid claim.
The weak interpretation, positing an analogy based on formal structural similarities, is supported as a more accurate description of the relationship.

Conclusions:

The free energy principle and Hamilton's principle of stationary action are best understood as analogous rather than equivalent.
This conclusion resolves ambiguity and provides a clearer theoretical foundation for understanding the free energy principle in relation to established physical principles.