# Difference between Steady State and Equilibrium

#### aman92ullah

Joined Jan 19, 2011
12
I was reading a text on semiconductor physics where I came across a description of 'steady state' and 'equilibrium'.
It said 'steady state' means value of state variables are independent of time.
And that when a system is in 'equilibrium', it means state variables must not change with time; this time being relatively long as compared to the time of interest.
It said the difference between equilibrium and steady state is that 'dissipation can occur in steady state, such as generation of heat in resistor'. Now wouldn't that mean temperature of that resistor rise and thus steady state is lost since temperature has risen?

This distinction of dissipation is not clear to me, even though I'm willing to put a cooling pad over the resistor to keep its temperature stable

#### daviddeakin

Joined Aug 6, 2009
207
It said the difference between equilibrium and steady state is that 'dissipation can occur in steady state, such as generation of heat in resistor'. Now wouldn't that mean temperature of that resistor rise and thus steady state is lost since temperature has risen?
It is assumed that the temperature has also risen to a steady value, so everything is now steady.

#### bretm

Joined Feb 6, 2012
152
In equilibrium, state variables are unchanging because the system is in a state of balance, e.g. charge carriers not moving because net forces on them are zero. Often the forces of thermal vibration are ignored when this description is used.

In steady state, state variables are unchanging even though the system is "out of balance". The system still experiences forces that may cause charge carriers to move, a.k.a. current, but the charge carrier density is unchanging everywhere because charges exiting a given infinitesimal volume are immediately replaced by charges entering the same volume from another direction.

The simplest example is a broken circuit vs a closed circuit consisting of a battery and a wire. The first is in equilibrium, the second is in a steady state.

If the circuit contained a resistor and a capacitor in series, it would neither be in equilibrium nor steady state because the capacitor voltage would continually change. But if the capacitor voltage reaches the battery voltage it would be in equilibrium (not steady state) because current would be zero.

#### aman92ullah

Joined Jan 19, 2011
12
Okay, so what I get from above is this:
If the system is in steady state, then the velocity of its charge carriers/particles is constant.
If the system is in equilibrium, this constant velocity is zero.

So in steady state you can have motion with state variables remaining unperturbed, while in equilibrium, you freeze the carriers in one place.

#### bretm

Joined Feb 6, 2012
152
First, the examples with charge carriers are just that: examples. It actually depends on what the state variables are.

But even assuming current is a state variable and therefore constant in the steady state, this does not imply constant charge carrier velocity. For an obvious counter-example, consider electrons accelerating through the vacuum in a tube diode or a CRT. Less obvious would be the acceleration occurring in the transition region between conductors of different bulk resistivity.

If those seem like odd-ball cases, consider that there are multiple such transition regions in a transistor (since you mentioned semiconductors), including the regions where the leads attached to the device, and that the strength of the e-field is different in a depletion region vs elsewhere.

In the case of state-state dissipation, the current is adding heat at the same rate as the environment is removing heat.

#### steveb

Joined Jul 3, 2008
2,436
It said the difference between equilibrium and steady state is that 'dissipation can occur in steady state, such as generation of heat in resistor'. Now wouldn't that mean temperature of that resistor rise and thus steady state is lost since temperature has risen?

This distinction of dissipation is not clear to me, even though I'm willing to put a cooling pad over the resistor to keep its temperature stable
The distinction of dissipation is not clear to me either. It seems to me that you can and do have dissipation in both steady state conditions and in dynamically changing conditions. So, it's not clear what your sources are trying to say.

As far as temperature rise, temperature itself is a state variable, or at least it should be considered to be a state variable with its own state equation. Hence, in order to have true steady state conditions, the time rate of change of temperature should be zero. This means that whatever is generating heat is being balance by a cooling process (radiation, convection or conduction).

#### studiot

Joined Nov 9, 2007
4,998
Can't say I'm very happy with any of the definitions so far.

That could be because the original definitions in the OP's book are more appropriate to thermodynamics than electricity.

In thermodynamics two connected bodies or systems are defined to be in equilibrium when they have the same temperature.

When they do not have the same temperature they are not in equilibrium and heat flows between them.

The flow of this heat may be steady or unsteady. The unsteady flow is akin to transients in electricity.

Take a circuit comprising a battery. This is not in equilibrium. It has a tendency to discharge, however slowly.

Connect the battery through an open switch to a discharged capacitor. The system is not in equilibrium.
Close the switch - a transient current flows - this is not a steady state current since it is continually changing with time.
Eventually electrical equilibrium between the battery and capacitor is reached and the current ceases and the system is in a steady state.

Now replace the capacitor with a resistor. The current never ceases, but never changes with time (battery self heating apart) so the system is always in a steady state once the cwitch is closed, but never in equilibrium since a current is flowing.

Now consider a signal generator. When we first swithc on we wait for it to warm up or stabilise. It is not in a steady state.
After warmiong up we assume the output both in frequency and voltage will remain steady for us to use.
However it is a voltage source and as such is not in equilibrium with out test circuit, otherwise it would not be able to provide the voltage and small signal current.

So it is possible for a system to be in equilibrium when the flow of the quantity of interest is steady at zero.
Or not in euqilibrium when the flow of the quantity of interest (heat, current whatever) can be steady or unsteady (transient).

It should be noted that the departure from equilibrium provides the capacity (drive or potential) for action but says nothing about the rate of flow or nature (steady or unsteady) of the flow qunatity.

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