Potencials

Potencials is a term used in several Romance languages (such as Catalan, Spanish, and Portuguese) to refer to potentials in a scientific sense, and in English it appears as the plural of potential. The core idea is a quantity that expresses capacity or possible effect, often functioning as a scalar field from which other quantities or flows derive.

In physics, a potential function, such as gravitational or electric potential, is a scalar field V(x) whose negative gradient yields the force density: F = -∇V. The associated potential energy represents the work required to assemble a system from a reference state. Electric potential difference, or voltage, is the work done per unit charge as one moves between two points.

In chemistry and thermodynamics, chemical potential μ is the partial molar Gibbs free energy. It governs diffusion and phase equilibria and depends on temperature, pressure, and composition. The gradients of chemical potential drive mass transport in mixtures and reactions.

In mathematics, potential theory studies harmonic and subharmonic functions, with classical problems such as Dirichlet and Neumann problems. Solutions are often constructed using potentials like Newtonian or Green’s functions to address Laplace’s equation Δφ = 0 or Poisson’s equation Δφ = f.

In economics and game theory, potential functions provide a way to capture the overall incentive structure of a system and are used to analyze equilibria in potential games, where individual incentives align with a global objective.