# Difference between stationary and steady state

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• Richard Parker
In summary, the problem is that I took the two concepts, stationary state and steady state, to be the same. Only now that I started to think if there is a difference.
Richard Parker
TL;DR Summary
Just wondering the difference of a stationary state and a steady state of a system.
I was recently working on a problem of Griffiths and in the solution's manual it used an argument to solve a diffential equation that caught my attention. It said that it would look first to the steady state solution of the ODE. I tought "All right, I get that" but when I got to translate the solution to a list of problems that must be ready for tomorow (I'm a physics undergrad at the UFPE from Brazil, so I must translate my answers to portuguese) I realized the I didn't know the difference between a stationary and a steady state. Don't both means that the system will not change over time? If not, what's the difference?

I'm not familiar with stationary state, but steady state means that nothing is changing with time at each spatial location.

anorlunda and Richard Parker
Suppose I have a system whose time response settles to sin(wt). The magnitude and frequency are constant. It is not really a steady state, but imaginative people might invent other adjectives to describe it.

One thing hard to get used to is that there are no language police in science or engineering. Sometimes definitions are strict. Other times sloppy. Other times fanciful; as in charmed quarks.

My definition of steady state agrees with @Chestermiller . Everything stops changing.

Richard Parker
A ring spinning about its symmetry axis at constant speed is in a steady state. Is it stationary? Typically I'd say no, but usage can vary.

I note that you quote Griffiths as using the term "steady state", but I don't think you say where you got "stationary" from. If it's a technical term then it ought to be defined somewhere (it has a precise meaning in general relativity, for example). Otherwise, as anorlunda says, there is often a certain sloppiness in language, even in science. That's why we have maths!

Ibix said:
A ring spinning about its symmetry axis at constant speed is in a steady state. Is it stationary? Typically I'd say no, but usage can vary.

I note that you quote Griffiths as using the term "steady state", but I don't think you say where you got "stationary" from. If it's a technical term then it ought to be defined somewhere (it has a precise meaning in general relativity, for example). Otherwise, as anorlunda says, there is often a certain sloppiness in language, even in science. That's why we have maths!
The problem is that I taked the two concepts, stationary state and steady state, to be the same. Only now that I started to think if there is a difference. In portuguese the word estacionário is used to describe a system that is not changing over time. If you translate estacionário to english you will get stationary. It looks like in english you have two words to describe the same concept that in portuguese is desbribed with only one. So I wondered if, since you have two words, maybe they represent similar, but not exactly the same, concepts. For example, in english we have speed and velocity, one is a scalar, the other a vector. In portuguese we have only one word to describe the same thing, which is velocidade. But speed and velocity are not the same thing. When we want to distinguish between the two we call speed o módulo da velocidade (the magnitude of the velocity). I could rephrase my question like this: If I'm looking for a steady state solution of a differential equation that describe a system and for a stationary solution of the same equation and system, am I looking for the same thing?

anorlunda said:
Suppose I have a system whose time response settles to sin(wt). The magnitude and frequency are constant. It is not really a steady state, but imaginative people might invent other adjectives to describe it.

One thing hard to get used to is that there are no language police in science or engineering. Sometimes definitions are strict. Other times sloppy. Other times fanciful; as in charmed quarks.

My definition of steady state agrees with @Chestermiller . Everything stops changing.
Yes, maybe I ran into a problem of semantics. I understand the problem of language on science, specially for me that have to translate the concepts to my native language. What worries me is the physical meaning of the concepts "stationary state of a system" and "steady state of a system". But, like you said, sometimes the definitions are sloppy.

words can have very specific meaning, based on context.

For example, see https://en.wikipedia.org/wiki/Stationary_state

A stationary state is a quantum state with all observables independent of time. It is an eigenvector of the Hamiltonian.[1]This corresponds to a state with a single definite energy (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences explained below.

If you have water in a closed container, with the gas phase above the liquid having the equilibrium humidity, it's a stationary situation (at least in macroscopic sense). If you have water in an open container, with more water dripping in from above with the same rate as the water evaporates, then it's a steady state.

The concept of steady state is often encountered in chemical or nuclear reaction kinetics.

The steady state solution to the differential equation is the solution at time goes to infinity.

For example if you have a pendulum (with some damping) and you put it in motion and release it, it will oscillate at the natural frequency. If you force the bob at a forcing frequency after you release it , it will initially oscillate at the natural frequency, but given time it will eventually be oscillating at the forcing frequency after the initial natural frequency damps away.

Stationary state is usually used in quantum mechanics. When a wavefunction is in a stationary state, it does not change in time, and ( I presume) it has never earlier been in any other state, and will never be in another state, unless the system changes. For example, a wavefunction can be in a stationary state in a finite well with length a, and the well can be extended to length 2a. This will change the system and the state will evolve. But without a change in the system, a wavefunction in a stationary state will stay in a stationary state. If a wavefunction ere initially in a linear superposition of two (or several) stationary states, that linear superposition (the coefficients) will evolve in time.

## What is the difference between stationary and steady state?

Stationary state refers to a state where there is no change or movement, while steady state refers to a state where there is a balance between inputs and outputs.

## How do stationary and steady state differ in terms of time?

Stationary state is a snapshot in time, while steady state is a continuous state that can be sustained over time.

## What are some examples of stationary and steady state in science?

An example of stationary state is a chemical reaction that has reached equilibrium, while an example of steady state is a predator-prey relationship in an ecosystem.

## Can a system be in both stationary and steady state at the same time?

No, a system can only be in one state at a time. However, a system can transition from a stationary state to a steady state over time.

## How do stationary and steady state affect the behavior of a system?

In a stationary state, the system is stable and there is no change, while in a steady state, the system is in balance and can sustain itself. Understanding these states can help predict the behavior of a system and how it may respond to changes.

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