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Jul
18
asked Introduction to differential forms in thermodynamics
Jul
11
revised List of Physical Toys
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Jul
11
revised List of Physical Toys
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Jul
11
awarded  Student
Jul
11
answered List of Physical Toys
Jul
11
answered List of Physical Toys
Jul
11
answered List of Physical Toys
Jul
11
asked List of Physical Toys
Jan
31
awarded  Commentator
Jan
31
comment Deriving an Expression for Entropy
The question is not how do you compute entropy (anyway one cannot generally compute the partition function), but how do you define entropy in statistical physics. I prefer the definition as $S = - \sum_i \; p_i \ln p_i$ ($- \int \rho \ln \rho \; d \Gamma$, $\text{Tr} \hat \rho \ln \hat \rho$). But following Boltzmann some use $\ln \Omega$ definition. I don't quite get that definition, at least in ensembles other than micro canonical. So I've asked how to derive one from the other partly because I wanted to understand that $\ln \Omega$ definition.
Jan
31
awarded  Scholar
Jan
31
comment Deriving an Expression for Entropy
Well, that's exact for microcanonical ensemble . The thing is that $\ln \Omega$ is used for canonical ensemble too. After a bit of thinking I think I got why it is valid and what does $\Omega$ mean for a canonical ensemble. Anyway I don't need it anymore, so I won't check my guess.
Jan
31
accepted Deriving an Expression for Entropy
Jan
30
comment What are conditions for the existence of a critical value (for a phase transition)?
Well, yes, however not a single value, but "a whole space dependent function". Though this function depends ultimatly on the kind of molecules, their structure, number of electrons, but it is equivalent to saying "every substance has it's own $T_c$".
Jan
30
comment What are conditions for the existence of a critical value (for a phase transition)?
The model can be defined with infinite number of numbers. For example if we are talking about simplest pair potential $f(r)$ it is a function $f : [0, \infty) \to \mathbb R$ --- that's a whole energy curve. Though I guess some rough estimation of $T_c $can be made based on a single energy value --- for example the depth of the potential.
Jan
30
comment Why does maximal entropy imply equilibrium?
Sometimes "entropy is maximum in equilibrium" is just put into the formulation of the second law. So what is the exact formulation of the second law you are using?
Jan
30
awarded  Supporter
Jan
30
comment What are conditions for the existence of a critical value (for a phase transition)?
For example, for Lennard-Jones model potential (sklogwiki.org/SklogWiki/index.php/Lennard-Jones_model) $T_c = 1.326 \varepsilon$ where $\varepsilon$ is the depth of the potential.
Jan
30
comment What are conditions for the existence of a critical value (for a phase transition)?
Ultimately for those kinds of systems you are taking $T_c$ and other thermodynamical properties are functions of the intermolecular potential. That is it is rather a whole function than a single energy value (scale). Thermodynamic properties depend on it via complex multidimensional integrals.
Jan
30
asked Deriving an Expression for Entropy