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Roger V.
Roger V.
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EE18
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In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:

Postulate II There exists a function ( called the entropy S) of the extensive parameters of any composite system, defined for all equilibrium states and having the foil owing property: The values assumed by the extensive parame- ters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states.

My question is: is it tacitly assumed that this entropy maximum is unique? That is, that there are not two different entropy-maximizing equilibrium states on the manifold? Perhaps this is related to toy models of the ferromagnet and what not that I've worked out in statistical mechanics courses without some deep understanding unfortunately.

Edit: I guess this question can be recapiutaled as, "can Callen's maximum ($S_i\leq S_{max}$) be interpreted as the existence of a strict global maximum ($S_i< S_{max}$)"?

In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:

Postulate II There exists a function ( called the entropy S) of the extensive parameters of any composite system, defined for all equilibrium states and having the foil owing property: The values assumed by the extensive parame- ters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states.

My question is: is it tacitly assumed that this entropy maximum is unique? That is, that there are not two different entropy-maximizing equilibrium states on the manifold? Perhaps this is related to toy models of the ferromagnet and what not that I've worked out in statistical mechanics courses without some deep understanding unfortunately.

In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:

Postulate II There exists a function ( called the entropy S) of the extensive parameters of any composite system, defined for all equilibrium states and having the foil owing property: The values assumed by the extensive parame- ters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states.

My question is: is it tacitly assumed that this entropy maximum is unique? That is, that there are not two different entropy-maximizing equilibrium states on the manifold? Perhaps this is related to toy models of the ferromagnet and what not that I've worked out in statistical mechanics courses without some deep understanding unfortunately.

Edit: I guess this question can be recapiutaled as, "can Callen's maximum ($S_i\leq S_{max}$) be interpreted as the existence of a strict global maximum ($S_i< S_{max}$)"?

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EE18
EE18
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Is an entropy maximum being unique a tacit assumption in thermodynamics?

In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:

Postulate II There exists a function ( called the entropy S) of the extensive parameters of any composite system, defined for all equilibrium states and having the foil owing property: The values assumed by the extensive parame- ters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states.

My question is: is it tacitly assumed that this entropy maximum is unique? That is, that there are not two different entropy-maximizing equilibrium states on the manifold? Perhaps this is related to toy models of the ferromagnet and what not that I've worked out in statistical mechanics courses without some deep understanding unfortunately.