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Gibbs Free Energy02:39

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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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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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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:
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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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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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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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Boosting MCTS With Free Energy Minimization.

Mawaba Pascal Dao1, Adrian M Peter2

  • 1Florida Institute of Technology, Melbourne, FL 32901, USA pdao2015@my.fit.edu.

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|September 22, 2025
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Summary
This summary is machine-generated.

This study introduces a novel planning framework combining Monte Carlo Tree Search (MCTS) with active inference to balance exploration and reward-seeking. The approach effectively reduces uncertainty while optimizing for goals in complex environments.

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Area of Science:

  • Artificial Intelligence
  • Computational Neuroscience
  • Robotics

Background:

  • Active inference, based on the free energy principle, explains agent behavior in uncertain environments.
  • Balancing exploration and goal-directed actions is crucial for intelligent agents.

Purpose of the Study:

  • To develop a new planning framework integrating Monte Carlo Tree Search (MCTS) with active inference.
  • To systematically reduce epistemic uncertainty while pursuing extrinsic rewards.

Main Methods:

  • Integration of MCTS with active inference objectives.
  • Utilizing the cross-entropy method (CEM) for action proposal optimization.
  • Blending expected rewards with information gain for free energy minimization.

Main Results:

  • The proposed planner maintains coherent estimates of value and uncertainty.
  • Demonstrated performance gains on continuous control tasks compared to existing methods.
  • Achieved computational tractability without sacrificing planning efficiency.

Conclusions:

  • The novel framework successfully combines exploration and exploitation using active inference and MCTS.
  • This approach offers a computationally tractable method for intelligent agents to navigate uncertainty.
  • The planner shows promise for applications in AI and robotics requiring adaptive decision-making.