It is therefore equal to the spontaneous entropy production in the system.

This is typical for expressions of the entropy production rates in general.

Since and this would result in which violates the condition that the entropy production is always positive.

Sensitivity to initial conditions and entropy production at the edge of chaos.

Entropy production is not incidental to the process of life, but rather the fundamental reason for its existence.

Using the continuity equations, the rate of entropy production may now be written:

They guarantee that the entropy production is positive.

It does not imply that the ensemble averaged entropy production is non-negative at all times.

The expression for the rate of entropy production in the first two cases will be derived in separate sections.

This product of ambient temperature and the (average) entropy production rate is called the dissipated power.

It is also possible that entropy production will cease and the universe will achieve heat death.

Present day life augments the entropy production of Earth by catalysing the water cycle through evapotranspiration.

This suggests a governing constraint by a principle of maximum rate of entropy production.

See the Article on entropy production.

Then, of all current distributions satisfying this condition, the steady state distribution makes the entropy production a maximum."

As the system is in equilibrium there are no irreversible processes so the entropy production is zero.

The Joule expansion gives a nice opportunity to explain the entropy production in statistical mechanical (microscopic) terms.

The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines.

An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production.

Thus entropy production is a measure of the irreversibility and may be used to compare engineering processes and machines.

The rate of entropy production for the above simple example uses only two entropic forces, and a 2x2 Onsager phenomenological matrix.

For example, in the linear irreversible cycle , the entropy production is positive but the principle of detailed balance does not hold.

See: Entropy production.

This is untrue, as consideration of the entropy production in a viscoelastic fluid subject to a sinusoidal time dependent shear rate shows.

In thermostatted nonequilibrium states that are close to equilibrium, the long time average of the dissipation function is equal to the average entropy production.