susceptibilities

Susceptibilities are material properties that quantify how a system responds to external stimuli, such as electric or magnetic fields, mechanical forces, or chemical and biological signals. In the linear regime, the response is proportional to the applied stimulus, with the proportionality factor called the susceptibility.

Magnetic susceptibility χ_m characterizes how magnetization M changes with an applied magnetic field H: M = χ_m H in many materials. Electric (or dielectric) susceptibility χ_e relates electric polarization P to an applied electric field E via P = ε0 χ_e E, and the dielectric permittivity ε = ε0(1 + χ_e), with the relative permittivity ε_r = 1 + χ_e.

In alternating fields, susceptibilities become frequency dependent and can be complex: χ(ω) = χ'(ω) − i χ''(ω). The real part describes dispersion, while the imaginary part describes losses. Models such as Debye or Lorentz describe the frequency dependence.

Thermodynamic susceptibilities are second derivatives of thermodynamic potentials, expressing how a system's state changes under small changes in conjugate variables. Examples include isothermal compressibility κ_T = −(1/V)(∂V/∂P)_T and magnetic susceptibility χ_T = (∂M/∂H)_T.

Higher-order susceptibilities χ^(2), χ^(3) describe nonlinear responses and are central in nonlinear optics, producing effects like second-harmonic generation and intensity-dependent refractive index.

Applications span physics, chemistry, materials science, and biology. Susceptibilities help predict material behavior in fields, assess dielectric and magnetic properties for devices, and quantify a system’s vulnerability or responsiveness to stimuli in biological and epidemiological contexts.

Limitations include nonlinearity, dissipation, and dependence on temperature, frequency, and history (hysteresis).