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How can the Fokker-Planck equation be used to solve problems in physics and chemistry? 

Morphing
Fokker–Planck equation
Master equation
H-theorem
Entropy production
Best insight from top research papers

The Fokker-Planck equation is a powerful tool for solving problems in physics and chemistry. It describes the evolution of probability density associated with stochastic differential equations. In higher dimensions, solving this equation using conventional methods becomes computationally prohibitive. However, a fast and scalable method has been introduced that approximates the solution using shape-morphing Gaussians with time-dependent means and covariances. This method, known as the method of reduced-order nonlinear solutions (RONS), ensures that the approximate solution stays close to the true solution of the equation for all times. The proposed method approximates both the transient dynamics and the equilibrium density. It can be viewed as an evolution on a finite-dimensional statistical manifold and has been shown to coincide with the Fisher information matrix. This method is interpretable, requires no training, and automatically satisfies all properties of a probability density . The Fokker-Planck equation also has applications in quantum physics, where it can be transformed into an equation of the Lindblad form. This transformation preserves the trace and positivity of the density operator and provides explicit expressions for the quantum equivalence of probability current and detailed balance . Additionally, the Fokker-Planck equation is used in non-equilibrium thermodynamics to describe systems with non-equilibrium physics behavior. It is connected to entropy generation and entropy production methods, allowing for a deeper understanding of energy generation and energy production in these systems . Finally, the Fokker-Planck equation is used to propagate uncertainty in dynamical systems driven by stochastic processes. A novel numerical method based on physics-based mixture models has been developed to solve the Fokker-Planck equation, capturing the tail behavior of the solution PDF and satisfying the necessary conditions of a proper PDF with unbounded support .

Answers from top 5 papers

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Papers (5)Insight
Book Chapter•DOI
Fokker-Planck Equations, Entropy Production and Entropy Generation: A Review
andre luis ferreira marques
04 Mar 2022
1 Citations
The paper does not provide specific examples of how the Fokker-Planck equation can be used to solve problems in physics and chemistry.
Journal Article•DOI
Numerical solution of the Fokker–Planck equation using physics-based mixture models
Armin Tabandeh, Neetesh Sharma, Leandro Iannacone, Paolo Gardoni 
01 Sep 2022-Computer Methods in Applied Mechanics and Engineering
4 Citations
The paper does not provide information on how the Fokker-Planck equation can be used to solve problems in physics and chemistry.
Quantum Fokker-Planck structure of the Lindblad equation
Mário J. de Oliveira
09 May 2023
The paper does not provide information on how the Fokker-Planck equation can be used to solve problems in physics and chemistry.
Open access•Posted Content•DOI
Quantum Fokker-Planck structure of the Lindblad equation
Шукурова Ф.Х.
09 May 2023
The provided paper does not directly discuss how the Fokker-Planck equation can be used to solve problems in physics and chemistry.
Open access•Posted Content•DOI
Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions
06 Jun 2023
The provided paper does not explicitly mention how the Fokker-Planck equation can be used to solve problems in physics and chemistry.

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