What is "steady state"

n. (context physics English) Any state that does not change over time, or is in a dynamic equilibrium

Steady state may refer to:

• Steady state (systems) an operating condition in thermodynamic and other systems or processes when variables stay constant as time passes.
  • Steady-state economy, an economy made up of a constant population size and a constant stock of physical wealth (capital).
  • Steady-state equilibrium (monetary theory), an economic situation where neutrality of money coincides with zero population growth.
  • Steady state (electronics), a state existing in a circuit or network when all transients have died away.
  • Steady state (chemistry), a central term in chemical kinetics.
  • Steady state (biochemistry), regarding ions across cell membranes
  • Steady state (physiology), also known as homeostasis, a system in which a particular variable is not changing but energy must be continuously added to maintain this variable constant.
  • Steady state (pharmacokinetics)
• Dynamic equilibrium commonly observed in dynamical systems.

It may also refer to:

• Steady State theory, a non-standard cosmological view developed in 1949 by Fred Hoyle and others as an alternative to the Big Bang theory.
• Steady state engine test stand, a type of application for engine testing.
• Microsoft Windows SteadyState, an imaging program for Microsoft operating systems.

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:

In discrete time, it means that the first difference of each property is zero and remains so:

p − p = 0 for all t.

The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a 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. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state.

In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. For example, while 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. a tank being drained or filled with fluid is a system in transient state, because its volume of fluid changes with time.

Often, a steady state is approached asymptotically. An unstable system is one that diverges from the steady state. See for example Linear difference equation#Stability.

In chemistry, a steady state is a more general situation than dynamic equilibrium. 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 a steady state, a system that is in a steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.

In ionic steady state, cells maintain different internal and external concentrations of various ionic species.

Cells are said to be in a steady state, NOT in an equilibrium. This means that there is a differential distribution of ions on either side of the cell membrane - that is, the amount of ions either side is not equal and therefore a charge separation exists. However, ions move across the cell membrane and almost constantly maintain a resting membrane potential; this is known as 'steady state.'

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.

In chemistry, 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). A simple example of such a system is the case of a bathtub with the tap running but with the drain unplugged: after a certain time, the water flows in and out at the same rate, so the water level (the state variable Volume) stabilizes and the system is in a steady state.

The steady state concept is different from chemical equilibrium. Although both may create a situation where a concentration does not change, in a system at chemical equilibrium, the net reaction rate is zero (products transform into reactants at the same rate as reactants transform into products), while no such limitation exists in the steady state concept. Indeed, there does not have to be a reaction at all for a steady state to develop.

The term steady state is also used to describe a situation where some, but not all, of the state variables of a system are constant. For such a steady state to develop, the system does not have to be a flow system. Therefore such a steady state can develop in a closed system where a series of chemical reactions take place. Literature in chemical kinetics usually refers to this case, calling it steady state approximation.

In simple systems the steady state is approached by state variables gradually decreasing or increasing until they reach their steady state value. In more complex systems state variable might fluctuate around the theoretical steady state either forever (a limit cycle) or gradually coming closer and closer. It theoretically takes an infinite time to reach steady state, just as it takes an infinite time to reach chemical equilibrium.

Both concepts are, however, frequently used approximations because of the substantial mathematical simplifications these concepts offer. Whether or not these concepts can be used depends on the error the underlying assumptions introduce. So, even though a steady state, from a theoretical point of view, requires constant drivers (e.g. constant inflow rate and constant concentrations in the inflow), the error introduced by assuming steady state for a system with non-constant drivers may be negligible if the steady state is approached fast enough (relatively speaking).