State variable, entropy, should be negative

The positive-and-negative property of a physical quantity is usually related to its physical meaning. The general convention is to use positive values to represent positive things and negative values to represent negative things. However, the state variable, entropy, is a strange physical quantity. From a macroscopic perspective, entropy represents the unavailable energy of the heat output of a thermodynamic system as it changes from an arbitrary state to a state in equilibrium with the environment, in short, the unavailable heat of the system. From a microscopic point of view, entropy represents the degree of disorder (chaos) in a system. Both the macroscopic and microscopic physical meanings of entropy indicate that it represents a negative thing. Therefore, entropy should be negative by its nature. However, historically, since Planck’s statement of Nernst’s heat theorem, entropy has always been taken for granted as a positive value. This is contrary to people’s cognitive habits, which adds to the mystery of entropy. Analyses indicate that Planck’s statement of Nernst’s heat theorem is not general and is valid only for single-component substances, such as perfect crystals. It is not an absolute fact that “entropy cannot be negative”. The Planck’s choice of a zero-temperature perfect crystal as the zero point of entropy is a non-physical operation and involves only a matter of convenience. Recently, based on the symmetry of reversible thermodynamics, a new equation of state for ideal solids has been established. Since entropy is explicitly included in the equation of state for ideal solids, the zero point of entropy cannot be chosen arbitrarily. The analysis from the thermodynamic stability and the verification of the property data show that entropy in the ideal solid equation of state must have a negative value. This physically specifies that the zero point of entropy should be the point of maximum entropy, i.e., the zero-pressure ideal gas limiting state. In fact, the ideal gas equation of state has a zero point of volume. That is the ideal solid limiting state (zero-volume state). At this zero point, the volume always takes a positive value. In brief, the zero point of volume of the ideal gas equation of state is the zero-temperature ideal solid, while the zero point of the entropy of the ideal solid equation of state is the zero-pressure ideal gas. The ideal solid equation of state is a creation of thermodynamic symmetry. The zero point of entropy, i.e., zero-pressure ideal gas is likewise a requirement of thermodynamic symmetry. The smaller the absolute value of negative entropy, the greater the unavailable energy of the system (the smaller the available energy) and the higher the degree of disorder of the system (the lower the degree of order). This is consistent with people’s cognitive habits. In addition, the zero-pressure ideal gas can be used as the zero point of entropy for both the ideal gas and the ideal solid equations of state, thus allowing a uniform orientation and division of the applicability of various practical equations of state between these two extreme equations of state. Unlike the choice of zero-temperature perfect crystal as the zero point of entropy, when zero-pressure ideal gas is used as the zero point of entropy, entropy takes a negative value, which is in accordance with the physical meaning of entropy and is also the requirement of thermodynamic symmetry. Taking a negative value for entropy is the physical, essential choice.