# Self-sustainability

Self-sustainability and self-sufficiency are overlapping states of being in which a person or organization needs little or no help from, or interaction with, others. Self-sufficiency entails the self being enough (to fulfill needs), and a self-sustaining entity can maintain self-sufficiency indefinitely. These states represent types of personal or collective autonomy.[1] On a national scale, a totally self-sufficient economy that requires little or no trade with the outside world is called an autarky. Absolute purity of personal self-sufficiency or national autarky is a theoretical concept rather than a reality, but relative degrees are observable in real-world examples.

Self-sustainability is a type of sustainable living in which nothing is consumed other than what is produced by the self-sufficient individuals. Examples of attempts at self-sufficiency in North America include simple living, homesteading, off-the-grid, survivalism, DIY ethic and the back-to-the-land movement.

Practices that enable or aid self-sustainability include autonomous building, permaculture, sustainable agriculture, and renewable energy. The term is also applied to limited forms of self-sustainability, for example growing one's own food or becoming economically independent of state subsidies. The self-sustainability of an electrical installation measures its degree of grid independence and is defined as the ratio between the amount of locally produced energy that is locally consumed, either directly or after storage, and the total consumption.[2]

A system is self-sustaining (or self-sufficient) if it can maintain itself by independent effort. The system self-sustainability is:

1. the degree at which the system can sustain itself without external support
2. the fraction of time in which the system is self-sustaining

Self-sustainability is considered one of the "ilities" and is closely related to sustainability and availability. In the economics literature, a system that has the quality of being self-sustaining is also referred to as an autarky.

## Formal definition

1. Let ${\displaystyle E}$ be a random variable that denotes the steady state number of external entities on which the system depends. Let ${\displaystyle p(v)}$ be the probability that the system depends on ${\displaystyle v}$ external entities, ${\displaystyle p(v)=P(E=v)}$. Then, the system self-sustainability, ${\displaystyle S}$, is ${\displaystyle S=p(0)}$.
2. Let ${\displaystyle e_{t}}$ be the expected time during which the system is self-sustaining from time 0 up to time ${\displaystyle t}$. Then, the system self-sustainability is the steady state fraction of time in which it is self-sustaining, ${\displaystyle S=\lim _{t\rightarrow \infty }{e_{t}}/{t}}$
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