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# 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:

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

The concept of steady state has relevance in many fields, in particular thermodynamics. 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 different 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.