ds

dS is a symbol that can denote different concepts in science, depending on the context. In thermodynamics and statistical mechanics, dS represents an infinitesimal change in entropy, a state function. For a reversible process, the differential of entropy satisfies dS = δQ_rev / T, where δQ_rev is the reversible heat transfer and T is the temperature. Entropy S is associated with the number of accessible microstates and the degree of disorder of a system; it tends to increase in spontaneous processes in accordance with the second law of thermodynamics. Because S is a state function, dS depends only on the initial and final states, not on the path taken between them.

In physics and cosmology, dS commonly refers to de Sitter space, a maximally symmetric solution of Einstein’s field equations with a positive cosmological constant Λ. The four-dimensional de Sitter space, dS4, can be described as a hyperboloid embedded in five-dimensional Minkowski space, or in various coordinate patches such as static or flat-slicing forms. The de Sitter radius l is related to the cosmological constant by Λ = 3 / l^2, and the spacetime has curvature characterized by R = 12 / l^2. It features a cosmological horizon with a Gibbons–Hawking temperature T = 1 / (2π l) and an associated horizon entropy S_h = π l^2 / G in Planck units. De Sitter space is a common model in early-universe inflationary theory and in discussions of dark-energy-driven expansion; it also appears in holographic contexts such as the proposed dS/CFT correspondence, though these ideas are less established than AdS/CFT.