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This relation defines @brief Langevin dynamics step: dX in the source section “Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW · @brief Langevin dynamics step: dX”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Takes a square root, requiring a nonnegative real radicand when interpreted over the reals. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read @brief Langevin dynamics step: dX as the quantity being defined or updated by this relation.
Uses a derivative or gradient to describe a rate of change or a direction of variation.
Takes a square root, requiring a nonnegative real radicand when interpreted over the reals.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
* @brief Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW
*/
inline double ou_step(double x, double theta, double mu, double sigma, double dW, double dt) {
return x + theta * (mu - x) * dt + sigma * dW;
}
/**
* @brief Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW
*/
inline double langevin_step(double x, double gradient, double temperature, double dW, double dt) {
return x - gradient * dt + std::sqrt(2.0 * temperature) * dW;
}
/**
* @brief Fokker-Planck probability update (discretized)
*/
inline double fokker_planck_step(double p, double p_left, double p_right,
double drift, double diffusion, double dx, double dt) {Exact original notation
@brief Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW