Steady state
Encyclopedia
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:
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.
. 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.
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.
, 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.
, 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.
System
System is a set of interacting or interdependent components forming an integrated whole....
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:
The concept of steady state has relevance in many fields, in particular thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
and economics. Steady state is a more general situation than
dynamic equilibrium
Dynamic equilibrium
A dynamic equilibrium exists once a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a steady state...
. If a system is in steady state, then the recently observed behavior of the system will continue into the future. In stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
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
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
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.
Economics
A steady state economy is an economy of relatively stable size. It features stable population and stable consumption that remain at or below carrying capacityCarrying capacity
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...
. 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
Robert Solow
Robert Merton Solow is an American economist particularly known for his work on the theory of economic growth that culminated in the exogenous growth model named after him...
and Trevor Swan
Trevor Swan
Trevor Winchester Swan was an Australian economist. He is best known for his work on the neoclassical model of economic growth, published simultaneously with that of Robert Solow, for his work on integrating internal and external balance, represented by the Swan diagram and for pioneering work in...
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
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
In chemistryChemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, and other chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...
, 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
Mass balance
A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...
). 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
Homeostasis (from Greek: ὅμοιος, hómoios, "similar"; and στάσις, stásis, "standing still") is the property of a system, either open or closedClosed system
-In physics:In thermodynamics, a closed system can exchange energy , but not matter, with its surroundings.In contrast, an isolated system cannot exchange any of heat, work, or matter with the surroundings, while an open system can exchange all of heat, work and matter.For a simple system, with...
, that regulates its internal environment and tends to maintain a stable, constant condition. Typically used to refer to a living organism
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...
, the concept came from that of milieu interieur
Milieu interieur
Milieu intérieur or interior milieu, from the French, milieu intérieur, is a term coined by Claude Bernard to refer to the extra-cellular fluid environment, and its physiological capacity to ensure protective stability for the tissues and organs of multicellular living organisms.-Origin:Claude...
that was created by Claude Bernard
Claude Bernard
Claude Bernard was a French physiologist. He was the first to define the term milieu intérieur . Historian of science I. Bernard Cohen of Harvard University called Bernard "one of the greatest of all men of science"...
and published in 1865. Multiple dynamic equilibrium adjustment and regulation mechanisms make homeostasis possible.
See also
- AttractorAttractorAn attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...
- Carrying capacityCarrying capacityThe carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...
- Control theoryControl theoryControl theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
- Dynamical systemDynamical systemA dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
- Ecological footprintEcological footprintThe ecological footprint is a measure of human demand on the Earth's ecosystems. It is a standardized measure of demand for natural capital that may be contrasted with the planet's ecological capacity to regenerate. It represents the amount of biologically productive land and sea area necessary to...
- Economic growthEconomic growthIn economics, economic growth is defined as the increasing capacity of the economy to satisfy the wants of goods and services of the members of society. Economic growth is enabled by increases in productivity, which lowers the inputs for a given amount of output. Lowered costs increase demand...
- Engine test standEngine test standAn engine test stand is a facility used to develop, characterize and test engines. The facility, often offered as a product to automotive OEMs, allows engine operation in different operating regimes and offers measurement of several physical variables associated with the engine operation.A...
- EquilibriumEquilibriumEquilibrium is the condition of a system in which competing influences are balanced. The word may refer to:-Biology:* Equilibrioception, the sense of a balance present in human beings and other animals...
- Evolutionary economicsEvolutionary economicsEvolutionary economics is part of mainstream economics as well as heterodox school of economic thought that is inspired by evolutionary biology...
- Growth curveGrowth curveA growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size, body height or biomass...
- Herman DalyHerman DalyHerman Daly is an American ecological economist and professor at the School of Public Policy of University of Maryland, College Park in the United States....
- HomeostasisHomeostasisHomeostasis is the property of a system that regulates its internal environment and tends to maintain a stable, constant condition of properties like temperature or pH...
- Limit-cycleLimit-cycleIn mathematics, in the area of dynamical systems, a limit-cycle on a plane or a two-dimensional manifold is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such...
- Limits to GrowthLimits to GrowthThe Limits to Growth is a 1972 book modeling the consequences of a rapidly growing world population and finite resource supplies, commissioned by the Club of Rome. Its authors were Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. The book used the World3 model to...
- Population dynamicsPopulation dynamicsPopulation dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes...
- SimulationSimulationSimulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
- State functionState functionIn thermodynamics, a state function, function of state, state quantity, or state variable is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state . A state function describes the equilibrium state of a system...
- Steady state economy
- Steady State theorySteady State theoryIn cosmology, the Steady State theory is a model developed in 1948 by Fred Hoyle, Thomas Gold, Hermann Bondi and others as an alternative to the Big Bang theory...
- Systems theorySystems theorySystems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...
- Thermodynamic equilibriumThermodynamic equilibriumIn thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...