Entrópia

Entrópia is a measure of the number of microscopic configurations corresponding to a macroscopic state, or more generally a measure of uncertainty or disorder in a system. The concept originated in 19th-century thermodynamics with Clausius and gained a statistical interpretation through Boltzmann, linking macroscopic observables to microscopic arrangements.

In thermodynamics, entropy S is a state function of a system’s macroscopic variables. For a reversible transfer, dS = δQ_rev / T, and the second law states that in an isolated system entropy tends not to decrease. Entropy is often expressed with units of energy per temperature, typically joules per kelvin (J/K). The law implies a preferred direction for spontaneous processes and characterizes equilibrium states.

Statistical mechanics provides microscopic foundations for entropy. Boltzmann’s formula S = k_B ln W relates entropy to W, the number of accessible microstates for a given macrostate, where k_B is Boltzmann’s constant. More general forms include Gibbs entropy, S = -k_B ∑ p_i ln p_i, with p_i the probability of microstate i. These expressions connect probability distributions to thermodynamic properties and explain how disorder arises from counting microstates.

In information theory, entropy measures uncertainty or information content. Shannon entropy H(X) = -∑ p(x) log p(x) quantifies average information per symbol, with base-2 logs yielding bits. There is a formal analogy between thermodynamic and informational entropy, linking physical processes to computational limits and energy costs of information handling.

Quantum generalizations include von Neumann entropy, S(ρ) = -Tr(ρ log ρ), where ρ is a quantum state. Entropy production describes irreversibility, and open systems can exchange entropy with their environment. The maximum entropy principle guides inference under uncertainty, and entropy remains central across physics, chemistry, and information sciences.