Editing Entropy (section)

=== The fundamental thermodynamic relation ===
{{Main|Fundamental thermodynamic relation}}
The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy <math display="inline">U</math> to changes in the entropy and the external parameters. This relation is known as the ''fundamental thermodynamic relation''. If external pressure <math display="inline">p</math> bears on the volume <math display="inline">V</math> as the only external parameter, this relation is:<math display="block">\mathrm{d} U = T\ \mathrm{d} S - p\ \mathrm{d} V</math>Since both internal energy and entropy are monotonic functions of temperature <math display="inline">T</math>, implying that the internal energy is fixed when one specifies the entropy and the volume, this relation is valid even if the change from one state of thermal equilibrium to another with infinitesimally larger entropy and volume happens in a non-quasistatic way (so during this change the system may be very far out of thermal equilibrium and then the whole-system entropy, pressure, and temperature may not exist).

The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system. Important examples are the [[Maxwell relations]] and the [[relations between heat capacities]].