In case there are other external parameters the above equation generalizes to:

It states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium.

In contrast, the second law states that for isolated systems, (and fixed external parameters) the entropy will increase to a maximum value at equilibrium.

Here the are the generalized forces corresponding to the external parameters .

Suppose that the system has some external parameter, x, that can be changed.

The entropy of a system depends on its internal energy and the external parameters, such as the volume.

If the volume is the only external parameter, this relation is:

The following code can easily be vectorized on compile time, as it doesn't have any dependence on external parameters.

But from a fixed Lorentz observer's viewpoint time remains a distinguished, absolute, external, global parameter.

We now consider an infinitesimal reversible change in the temperature and in the external parameters on which the energy levels depend.