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Related Concept Videos

Dynamic Equilibrium02:20

Dynamic Equilibrium

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Solution Equilibrium and Saturation01:59

Solution Equilibrium and Saturation

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Imagine adding a small amount of sugar to a glass of water, stirring until all the sugar has dissolved, and then adding a bit more. You can repeat this process until the sugar concentration of the solution reaches its natural limit, a limit determined primarily by the relative strengths of the solute-solute, solute-solvent, and solvent-solvent attractive forces. You can be certain that you have reached this limit because, no matter how long you stir the solution, undissolved sugar remains. The...
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Free Energy and Equilibrium02:56

Free Energy and 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 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...
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Calculating the Equilibrium Constant02:46

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The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
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Calculating Equilibrium Concentrations02:05

Calculating Equilibrium Concentrations

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Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more...
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The Equilibrium Binding Constant and Binding Strength02:18

The Equilibrium Binding Constant and Binding Strength

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The equilibrium binding constant (Kb) quantifies the strength of a protein-ligand interaction. Kb can be calculated as follows when the reaction is at equilibrium:
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A Physics-Informed Neural Network (PINN) Approach to Over-Equilibrium Dynamics in Conservatively Perturbed Linear

Abhishek Dutta1, Bitan Mukherjee2, Sk Aftab Hosen2

  • 1Department of Chemical Engineering, Izmir Institute of Technology, Izmir 35430, Turkey.

Entropy (Basel, Switzerland)
|January 28, 2026
PubMed
Summary
This summary is machine-generated.

Physics-informed neural networks (PINNs) accurately simulate chemical reaction dynamics, capturing transient over-equilibrium concentration extrema without extensive data. This approach ensures physical conservation laws are met efficiently.

Keywords:
conservatively perturbed equilibriumcyclic and acyclic mechanismsfinite-time thermodynamicsover-equilibrium dynamicsphysics-informed neural network

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Area of Science:

  • Chemical kinetics
  • Computational chemistry
  • Artificial intelligence in science

Background:

  • Conservatively perturbed equilibrium (CPE) experiments reveal transient concentration extrema exceeding steady-state values.
  • Simulating these over-equilibrium dynamics in chemical reaction networks is computationally challenging, often requiring extensive time-series data.

Purpose of the Study:

  • To introduce a physics-informed neural network (PINN) framework for simulating over-equilibrium dynamics in linear chemical reaction networks.
  • To demonstrate the PINN's ability to accurately capture transient concentration extrema without extensive time-series data.

Main Methods:

  • Developed a PINN framework incorporating reaction kinetics, stoichiometric invariants, and equilibrium constraints into the loss function.
  • Ensured the PINN solution strictly adheres to physical conservation laws.
  • Applied the PINN to three- and four-species reversible reaction mechanisms (acyclic and cyclic).

Main Results:

  • The PINN surrogate accurately reproduced results from conventional ODE integration.
  • The model successfully captured characteristic early concentration extrema (maxima/minima) and subsequent relaxation to equilibrium.
  • High accuracy was achieved in predicting the timing and magnitude of extrema while preserving total mass.

Conclusions:

  • The physics-informed approach enables accurate simulation of over-equilibrium dynamics with minimal data.
  • PINNs offer a parameter-efficient and physically constrained method for modeling complex chemical systems.
  • This framework demonstrates the potential of AI in advancing computational chemistry and reaction dynamics.