Izotróp

Izotróp, or isotropic in English, describes the property of being the same in all directions. The term comes from Greek isos, meaning equal, and tropos, meaning way or direction. In practice, isotropy implies rotational symmetry of a material’s properties or of a physical field.

In physics and engineering, isotropy means that a property does not depend on the direction of measurement. For optical media, an isotropic material has a refractive index that is the same for light traveling in any direction. In acoustics and electromagnetism, wave speeds and field responses are direction-independent in such media.

In elasticity, an isotropic solid has the same mechanical response in every direction. Its constitutive relation can be described with two independent elastic constants (commonly the Lamé constants, or equivalently Young’s modulus and Poisson’s ratio). This results in stress-strain behavior that is invariant under rotations. By contrast, most crystalline materials are anisotropic, showing direction-dependent properties.

In diffusion and transport phenomena, an isotropic medium features a diffusion tensor proportional to the identity, so fluxes align with concentration gradients regardless of direction. This contrasts with anisotropic diffusion, where spreading rates vary with direction.

In cosmology, the large-scale structure of the universe is modeled as isotropic (and homogeneous), meaning properties are statistically the same in all directions. Observations of the cosmic microwave background reveal small anisotropies that encode early-universe information, but overall isotropy remains a guiding assumption.

Examples of naturally isotropic materials include gases, liquids, and many amorphous solids; many real-world materials exhibit anisotropy due to crystal structure or texture.