potentiels

Potentiels is the French plural form of potentiel and is used in several scientific disciplines to denote scalar fields that encode potential energy or potential functions. In physics and engineering, a potential field is a scalar function V(x) such that the force is the negative gradient: F = −∇V. The potential is defined up to an additive constant, since only differences in potential have physical significance. When the force is conservative, work around a closed path vanishes and the potential energy difference governs the motion within the field.

Electric potential, measured in volts, relates to the electric field by E = −∇V. Gravitational potential per unit mass, often denoted Φ, satisfies g = −∇Φ, and gravitational potential energy is mΦ. Potential differences drive many phenomena in electrostatics and gravitation, with equipotential surfaces representing loci of equal potential.

In mathematics, potential theory studies potentials as fundamental objects tied to harmonic functions and the Laplace operator. The Newtonian or Coulomb potential acts as a Green’s function for the Laplacian in Euclidean space; solutions to ∇^2u = 0 are harmonic and obey the maximum principle. The theory connects to complex analysis, probability (through Brownian motion), and numerical methods such as boundary element methods.

In other contexts, potentiels appear as membrane potentials in neuroscience, describing the voltage difference across neural membranes, and as potential energy surfaces in chemistry and materials science, which guide reaction dynamics and phase behavior. The term thus spans physical, mathematical, and applied domains, reflecting the central role of potential concepts in modeling forces and energies.