# Entropic Functions

1. Apr 7, 2005

### Spin_Network

Can Entropy be reduced from a Macro Area (large quantity?), to a Micro Quantity, individual 'area' components?

If so would this process be reductionism or Separationism?

2. Apr 7, 2005

### dextercioby

It would be nonsense.Entropy is a statistical quantity defined on statistical ensembles...

Daniel.

3. Apr 7, 2005

### Crosson

This is not true, entropy is defined for any system for which we can recognize "macrostates" and "microstates".

You might have meant that the second law of thermodynamics would be nonsense if applied to a system other than a statistical ensemble.

What exactly are you asking? Can entropy be defined for small systems (yes)? Could it be meaningful to consider the entropy of various subsytems (yes)? Please try and rephrase the question.

4. Apr 7, 2005

### Spin_Network

Of course the natural path for Entropy is to spread out from a compact domain, to one that is less compact, I believe the standard stance is:Energy, in whatever form, tends to Equilibriate from an out_of_equlibrium state, to one that is closer to Equilibrium.

A volume/area of matter that is close to an Equilibrium state, can only get closer to Equilibrium, by interaction with its surrounding Area/Volume.

So a small Area that has energy present, if it is reduced further, ie in Stringtheory for instance, the Seperation of Componant energy, actually increase's the Energy value.

Lets start to reduce an energy from a particle of certain size, to one of a lesser size, from a Proton to an individual Quark, or from an individual Quark to a single string?

In Entropy terms, this is creating a Non-Equilibriated starting point?..the potential of which can interact with the surrounding Area/..do you agree?

So the "nonsense" now becomes apparent..please enlighten me!

Define the stastistical ''quantity" for change of 'one_MACRO_AREA->to_one micro_area'.

5. Apr 7, 2005

### dextercioby

$$S_{stat,class.stat.virtual ensemble}=:-k\langle \ln \rho\rangle _{\rho}$$ (1)

This is the definition.

The definition of $\rho$...

$$\rho (x,0) =:\lim_{\Omega_{\mathcal{D}} \rightarrow 0 ,x\in \mathcal{D}} \frac{1}{\Omega_{\mathcal{D}}} \left(\lim_{\mathcal{N}\rightarrow +\infty}\frac{\mathcal{N}\left(\mathcal{D}_{t=0}\right)}{\mathcal{N}}\right)$$

The dependence of the probability density of a classical miscrostate "x" of the macrostate is postulated.

Correctly

$$\rho=\rho\left(microstate,time;macrostate\right)$$

Einstein did it.We may call (1) Gibbs' entropy,but Einstein provided the concept that definition relies on:virtual statistical ensemble...

Daniel.

Last edited: Apr 7, 2005
6. Apr 7, 2005

### Spin_Network

Thanks, so the Phase transition of an Ensemble is governed by the above Equation?..is Gibbs Entropy equivilent for all Volumes?

7. Apr 7, 2005

### dextercioby

Volume is an mechanical extensive parameter involved in the description of a macrostate of a closed (constant volume) thermodynamical system.So,yes,entropy is a function of volume.

Macroscopical volume...The volume of a domain in $\mathbb{R}^{3}$ ...

Daniel.