irreversibility

Irreversibility refers to processes that proceed in a preferred direction in time and cannot be readily reversed to restore the original state. In thermodynamics, irreversibility is tied to the second law: in an isolated system, entropy tends to increase, so processes such as mixing gases, diffusion, friction, and spontaneous heat flow from hot to cold are effectively one-way. Real-world irreversibility is also observed in chemical reactions proceeding toward equilibrium and in the damping of mechanical systems, where usable energy is dissipated as heat.

Fundamental equations governing particles and fields are mostly time-reversal invariant, which means they do not by themselves enforce a preferred temporal direction. Irreversibility therefore arises from statistical behavior and the practical impossibility of tracking enormous numbers of microscopic degrees of freedom. Initial conditions, interactions with surroundings, and coarse-grained descriptions lead to a macroscopic arrow of time.

Two classic issues are Loschmidt's paradox, which asks why entropy increases if microscopic laws are reversible, and Poincaré recurrence, which shows that finite systems can revisit prior states given enough time. In statistical mechanics, Boltzmann's H-theorem offers a framework for entropy growth under assumptions such as molecular chaos, though it does not fully resolve all conceptual questions.

Beyond thermodynamics, irreversibility has implications for information and computation. Erasing information is associated with entropy production per Landauer's principle, implying a physical cost to irreversible operations. Irreversibility thus spans physics, chemistry, and information theory, and it characterizes practical limits on energy dissipation, time control, and the evolution of complex systems.