Steady state

For other uses, see Steady state (disambiguation).

A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:

$\frac{\partial p}{\partial t} = 0$

The concept of steady state has relevance in many fields, in particular thermodynamics and economics. Steady state is a more general situation than dynamic equilibrium. If a system is in steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant.

In many systems, steady state is not achieved until some time has elapsed after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period.

While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in steady state, a system that is in steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.

For example: The flow of fluid through a tube, or electricity through a network, could be in a steady state because there is a constant flow of fluid, or electricity. Conversely, a tank which is being drained or filled with fluid would be an example of a system in transient state, because the volume of fluid contained in it changes with time.

Applications

Economics

Main article: Steady state economy

A steady state economy is an economy of relatively stable size. It features stable population and stable consumption that remain at or below carrying capacity. The term typically refers to a national economy, but it can also be applied to the economic system of a city, a region, or the entire planet. Note that Robert Solow and Trevor Swan applied the term steady state a bit differently in their economic growth model. Their steady state occurs when investment equals depreciation, and the economy reaches equilibrium, which may occur during a period of growth.

Electronics

Main article: Steady state (electronics)

In electronics, steady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important.

Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics. Periodic steady-state solution is also a prerequisite for small signal dynamic modeling. Steady-state analysis is therefore an indispensable component of the design process.

Chemistry, thermodynamics, and other chemical engineering

Main articles: Steady state (chemistry) and Steady state (biochemistry)

In chemistry, thermodynamics, and other chemical engineering, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, there must be a flow through the system (compare mass balance). One of the simplest examples of such a system is the case of a bathtub with the tap open but without the bottom plug: after a certain time the water flows in and out at the same rate, so the water level (the state variable being Volume) stabilizes and the system is at steady state. Of course the Volume stabilizing inside the tub depends on the size of the tub, the diameter of the exit hole and the flowrate of water in. Since the tub can overflow and eventually a steady state can be reached where the water in equals the overflow plus the water out through the drain.

A steady state flow process requires conditions at all points in an apparatus remain constant as time changes. There must be no accumulation of mass or energy over the time period of interest. The same mass flow rate will remain constant in the flow path through each element of the system. Thermodynamic properties may vary from point to point, but will remain unchanged at any given point.

Physiology

Main article: Homeostasis

Homeostasis (from Greek: ὅμοιος, hómoios, "similar"; and στάσις, stásis, "standing still") is the property of a system, either open or closed, that regulates its internal environment and tends to maintain a stable, constant condition. Typically used to refer to a living organism, the concept came from that of milieu interieur that was created by Claude Bernard and published in 1865. Multiple dynamic equilibrium adjustment and regulation mechanisms make homeostasis possible.

See also

• Attractor
• Carrying capacity
• Control theory
• Dynamical system
• Ecological footprint
• Economic growth
• Engine test stand
• Equilibrium
• Evolutionary economics
• Growth curve
• Herman Daly
• Haemostasis
• Limit-cycle
• Limits to Growth
• Population dynamics
• Simulation
• State function
• Steady state economy
• Steady State theory
• Systems theory
• Thermodynamic equilibrium