The term adaptation is used in biology in relation to how living beings adapt to their environments, but with two different meanings. First, the continuous adaptation of an organism to its environment, so as to maintain itself in a viable state, through sensory feedback mechanisms. Second, the development (through evolutionary steps) of an adaptation (an anatomic structure, physiological process or behavior characteristic) that increases the probability of an organism reproducing itself (although sometimes not directly).[citation needed]

Generally speaking, an adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts. Feedback loops represent a key feature of adaptive systems, allowing the response to changes; examples of adaptive systems include: natural ecosystems, individual organisms, human communities, human organizations, and human families.

Some artificial systems can be adaptive as well; for instance, robots employ control systems that utilize feedback loops to sense new conditions in their environment and adapt accordingly.

Every adaptive system converges to a state in which all kind of stimulation ceases.[1]

A formal definition of the Law of Adaptation is as follows:

Given a system $S$, we say that a physical event $E$ is a stimulus for the system $S$ if and only if the probability $P(S \rightarrow S'|E)$ that the system suffers a change or be perturbed (in its elements or in its processes) when the event $E$ occurs is strictly greater than the prior probability that $S$ suffers a change independently of $E$:

$P(S \rightarrow S'|E)>P(S \rightarrow S')$

Let $S$ be an arbitrary system subject to changes in time $t$ and let $E$ be an arbitrary event that is a stimulus for the system $S$: we say that $S$ is an adaptive system if and only if when t tends to infinity $(t\rightarrow \infty)$ the probability that the system $S$ change its behavior $(S\rightarrow S')$ in a time step $t_0$ given the event $E$ is equal to the probability that the system change its behavior independently of the occurrence of the event $E$. In mathematical terms:

1. - $P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0$
2. - $\lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')$

Thus, for each instant $t$ will exist a temporal interval $h$ such that:

$P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')$