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Entropy is a thermodynamic property just like pressure, volume, or temperature. Therefore, it connects the microscopic and the macroscopic world view. Boltzmann's principle is regarded as the foundation of statistical mechanics .
Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume. This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials ).
Figure 1. A thermodynamic model system. Differences in pressure, density, and temperature of a thermodynamic system tend to equalize over time. For example, in a room containing a glass of melting ice, the difference in temperature between the warm room and the cold glass of ice and water is equalized by energy flowing as heat from the room to the cooler ice and water mixture.
This relationship was expressed in an increment of entropy that is equal to incremental heat transfer divided by temperature. Entropy was found to vary in the thermodynamic cycle but eventually returned to the same value at the end of every cycle. Thus it was found to be a function of state, specifically a thermodynamic state of the system.
The relationship between entropy, order, and disorder in the Boltzmann equation is so clear among physicists that according to the views of thermodynamic ecologists Sven Jorgensen and Yuri Svirezhev, "it is obvious that entropy is a measure of order or, most likely, disorder in the system."
While temperature is an intensive measure, this energy expresses the concept as an extensive property of the system, often referred to as the thermal energy, [13] [14] The scaling property between temperature and thermal energy is the entropy change of the system.
At absolute zero temperature, the system is in the state with the minimum thermal energy, the ground state. The constant value (not necessarily zero) of entropy at this point is called the residual entropy of the system. With the exception of non-crystalline solids (e.g. glass) the residual entropy of a system is typically close to zero. [2]
where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the second law inequality from above. It therefore follows that any net work δw done by the sub-system must obey