Entropy postulate definition

The idea is developed by postulating a function of the extensive parameters that tends to a maximum for any composite system that approaches a state of equilibrium on removal of an internal constraint. This function, to be called the entropy S, is defined only for equilibrium states where it assumes definite values. The basic problem of thermodynamics may therefore be considered solved once the entropy is specified in terms of a fundamental relation as a function of the extensive parameters. ... 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

We shall now postulate a mathematical definition of entropy, in terms of the/t7s, wliicIT Is larfflfih the case of a random distribution small otherwise. This definition is... 

Similarly, if one is interested in a macroscopic thermodynamic state (i.e., a subset of microstates that corresponds to a macroscopically observable system with bxed mass, volume, and energy), then the corresponding entropy for the thermodynamic state is computed from the number of microstates compatible with the particular macrostate. All of the basic formulae of macroscopic thermodynamics can be obtained from Boltzmann s definition of entropy and a few basic postulates regarding the statistical behavior of ensembles of large numbers of particles. Most notably for our purposes, it is postulated that the probability of a thermodynamic state of a closed isolated system is proportional to 2, the number of associated microstates. As a consequence, closed isolated systems move naturally from thermodynamic states of lower 2 to higher 2. In fact for systems composed of many particles, the likelihood of 2 ever decreasing with time is vanishingly small and the second law of thermodynamics is immediately apparent. 

There are two keys to this generalization, whereby a rational definition for entropy of nonequilibrium states is obtained. First, a more general second law is postulated, based on the property availability. (The availability at any state of a system reflects the extent to which it could affect any other system.) The second key is the introduction of other integrating factors, in addition to temperature, in order to deduce the fundamental differential property relationship (i.e., Gibbs equation.)... 

Step 8. Postulate Unear relations between these fluxes and forces that obey the Curie restriction, and demonstrate that entropy generation can be expressed as a positive-definite quadratic form. 

Now we consider an arbitrary process p passing arbitrary states between two such states—initial a, and final ct/. Choosing the (stable equilibrium) reference state ao and a process p, from cto to oi, we can regard the process p, followed by process p as a combined process connecting ao and a/. Therefore it follows from the definition (1.31) for Sf (entropy in the state cry with ao as a reference state) and postulate S2 that... 

It is important to note that while Eq. (10.7.10) has been derived for the equilibrium state, it is generally postulated to hold as well for any other configuration of the system, and so serves as a fundamental definition for the entropy. 

The thermodynamic functions of a dilute gas can be calculated from the molecular partition function of the gas. The necessary formulas are based on the postulates of statistical mechanics and on the definition of the statistical entropy... 

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