# Which has least entropy- living organism or same mass as chrystal?

1. May 13, 2013

### bcrelling

Which has the least entropy?

A 1kg diamond vs 1kg living organism

I've gather that living things are generally at a state of low entropy compared to the same matter in other configurations- as though complexity goes hand in hand with low entropy. Yet a perfect chrystal is supposedly low entropy(and at mimimal complexity). What am I confusing?

2. May 13, 2013

### Andrew Mason

Entropy is a thermodynamic state function. We measure entropy as the logarithm of the number of different microstates that a system can have while still having the same thermodynamic (macro) state.

A living cell can have many different states and still be the same living cell. A crystal can have only very few states and still be the same crystal. So the crystal has lower entropy than a cell.

While it is alive, a cell converts heat flow into mechanical work, so it is really a heat engine. Heat engines turn high entropy thermal energy into low entropy forms of energy (eg. electrical or gravitational potential energy - lifting a weight). It does this by increasing the entropy of the surroundings, overall (second law). But this does not mean that the engine itself has low entropy. It just provides a means of creating low entropy locally.

AM

3. May 17, 2013

### bcrelling

Thanks that's very elucidating.
I see that complexity doesn't go hand-in hand with low entropy at all, if anything the opposite is more likely to be true.

Is this statement true?
"The amount of information required to decribe a system exactly, is directly proportional to its entropy"

And if so, could Occam's Razor be considered a notion that low entropy theories(theories requiring the least information to express) as preferable to high entropy ones?

4. May 17, 2013

### Andrew Mason

The term 'entropy' was used by Shannon in developing information theory. It has a similar mathematical form to thermodynamic entropy. But the concepts are different. There is no direct relationship between information theory and thermodynamics. At least there is no relationship that will help you understand either concept better.

Occam's Razor is a general statement and is frequently not true. The second law of thermodynamics is always true.

AM

5. May 17, 2013

### Jano L.

This is not justified. A living cell is extremely complex system out of thermodynamic equilibrium. There is no easy way to ascribe entropy to it, so it makes no sense to say it is higher or lower than that of crystal.

6. May 18, 2013

### Andrew Mason

Why not? Just use the statistical definition of entropy: S = k ln W (k = the Boltzmann constant) where W is the number of microstates for a given macrostate.

For a living cell, the macrostate is the same for any arrangement of atoms contained in the cell provided it still functions as a living cell. It can have many different microstates. If that were not the case, it would not be alive. Within a cell, molecules are being created and modified all the time. They are moved around, transported to different organelles within the cell. All those different arrangements of molecules within a living cell are different microstates for the same macrostate.

It seems to me that the number different arrangements of atoms within a crystal, while still maintaining the crystal structure, would be much less.

AM

7. May 18, 2013

### Jano L.

In thermodynamics, the word macrostate refers to a set of easily measurable quantities. It is hard replace U,V by "it functions as a living cell". That is too vague - does a dying cell qualify? It still performs some functions of the living cell, osmosis, chemical reactions do not just stop instantly. We end up in the problem how to measure state of life/death and this is too difficult to apply any simple formula like S = k ln W.

8. May 18, 2013

### Andrew Mason

We do not need an absolute measure of the number of microstates. The question was whether a crystal had lower entropy than a living cell. We just have to compare the number of available microstates of a living cell to the number of available microstates of a crystal.

Let's say we could cool a living cell to absolute 0 (at some point, T, it ceases living/changing so cooling from that point to 0K simply preserves its overall structure at T). We do the same for a crystal. At 0K the crystal will have 0 entropy. There is only one microstate for the crystal. But the cell can have as many microstates at 0K that it could have had at T. So its entropy is not 0.

AM

Last edited: May 18, 2013
9. May 18, 2013

### Jano L.

How many is that?

Number of microstates is not to be calculated from one realization of a cell, because such always has only one microstate.

This number is to be calculated as the number of different microstates that are compatible with the macrostate.

How do you define macrostate of a cell?

My point is that there is no sense in talking about relevant microstates of a cell if we cannot even define its macrostate.

10. May 20, 2013

### bcrelling

Whatever the definition for entropy of a living organism might be, wouldn't it necessarily have to have higher entropy than a perfect crystal, considering that a perfect crystal is accepted as having lower entropy than all other configurations of matter?

On the other hand, we can reason that living organisms are far from high entropy systems, is that increasing the entropy in a living organism(via heat/radiation/mechanical trauma) often results in death. Ah but then we are stuck with what a thermodynamic definition of being alive/dead is! It's a good question and probably what I should have asked in the first place.

11. May 20, 2013

### Jano L.

No, because we can compare only numbers we are sure exist. If we had some general definition of entropy applicable both to crystal and a living organism, we could try to find out which one has higher entropy. But without such definition, the comparison is impossible.

12. May 20, 2013

### bcrelling

Could a living organism be "A heat engine which indefinitely maintains low internal entropy"?

This would be true for DNA, as there is a very limited variety of DNA combinations which will constitute its own preservation. And though DNA does change through selection of beneficial mutations, these changes reduce the entropy of the matter caught up in the process (e.g. 100kg of cells has fewer configurations to make a functioning human being than 100kg of cells constituting a barrel of plankton).

A refridgerator would not fit this definition as without maintenance/servicing very soon succumbs to the ravages of entropy in time, whereas living DNA has been going for 4billion years.

This might be the advantage a living organism has over a perfect crystal- life actively resists entropy whereas a perfect crystal cannot.