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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...
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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...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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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).
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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).
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Free energy—abbreviated as G for the scientist Gibbs who discovered it—is a measurement of useful energy that can be extracted from a reaction to do work. It is the energy in a chemical reaction that is available after entropy is accounted for. Reactions that take in energy are considered endergonic and reactions that release energy are exergonic. Plants carry out endergonic reactions by taking in sunlight and carbon dioxide to produce glucose and oxygen. Animals, in turn, break...
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Exploring Caspase Mutations and Post-Translational Modification by Molecular Modeling Approaches
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Monte Carlo algorithm for free energy calculation.

Sheng Bi1,2, Ning-Hua Tong1,2

  • 1Department of Physics, Renmin University of China, 100872 Beijing, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2015
PubMed
Summary
This summary is machine-generated.

We developed a new Monte Carlo algorithm for calculating free energy by sampling configuration space. This method accurately computes the Ising model

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Free energy calculation is crucial in statistical mechanics.
  • Existing methods like Wang-Landau sampling have limitations.

Purpose of the Study:

  • To introduce a novel Monte Carlo algorithm for free energy calculation.
  • To validate the algorithm's performance against exact solutions.

Main Methods:

  • Configuration space sampling Monte Carlo algorithm.
  • Temperature scan (upward/downward) for free energy F(T).
  • Implementation for Ising model on square and triangular lattices.

Main Results:

  • Excellent agreement between calculated and exact free energies.
  • Algorithm properties analyzed and compared to Wang-Landau.
  • Demonstrated applicability to general classical statistical models.

Conclusions:

  • The proposed Monte Carlo method provides accurate free energy calculations.
  • It offers an alternative to energy space sampling methods.
  • Potential for extension to quantum systems exists.