Stationary state

A system or process is said to be in steady state if the variables that define its behavior, with respect to time, remain invariant. The mathematical expression would state that for those properties p of the system, the partial derivative of p with respect to time is null:

▪ ▪ p▪ ▪ t=0for everythingt.{displaystyle {frac {partial p}{partial t}}}=0quad {text{for all}}t. !

In discrete periods of time, this implies that:

pt− − pt− − 1=0for everythingt.{displaystyle p_{t}-p_{t-1}=0quad {text{for all}}t. !

The concept of steady state becomes relevant in fields such as thermodynamics and engineering.
In particular, a physical system is in steady state when its characteristics do not vary with time. The theories of electrostatics and magnetostatics, among others, are based on this foundation. It is usually the situation to consider in a large part of the assumptions of thermodynamics. The steady state is also known as the state in which nature is (state it is in).

In chemical kinetics, the steady state can also be used to determine the rate constant of a reaction through various experiments in which it can be assumed that a concentration of some product or reactant does not change.

It is also said that a system is in a stationary state if the variations over time of the physical quantities are periodic and repeat themselves in an identical manner at each period. This is the case, for example:

• of systems in which there are waves whose amplitude and frequency does not vary, as in an interferometer.
• electric circuits fed with alternative generators, once the transient phenomena have disappeared.

It is the reference state in thermodynamics of irreversible processes. The stationary state of an open system that is in equilibrium is defined as the one in which the state variables (temperature, volume, pressure, etc.) do not change and, therefore, the functions of state (entropy, enthalpy, etc.). The stationary state is a state of minimum production of entropy (principle of minimum energy).