# B 2nd law of thermodynamics -- why?

1. Mar 25, 2016

### Einstein's Cat

I am aware of the Second Law of Theromodynamics and I understand it to a certain extent, although still I am burdened with the frustration of being ignorant to why such a law exists. Please assist me.

2. Mar 25, 2016

### QuantumQuest

It is an empirical finding and it is accepted as an axiom of thermodynamics. Its microscopic origin is explained by statistical thermodynamics. It basically has to do with the irreversibility of a thermodynamical process, something observed in our macroscopic reality.

3. Mar 25, 2016

### Einstein's Cat

Why does this irreversibility exist?

4. Mar 25, 2016

### QuantumQuest

Because of the asymmetric character of thermodynamic operations.

5. Mar 25, 2016

### Khashishi

Consider a box of six sided dice. Initially, they all have "1" facing up. Now shake the box very gently, so dice only have a small probability of flipping over time. As time passes, the dice look more and more randomly distributed. Entropy can be thought of as your lack of knowledge about a system. If you know the initial state exactly, then the initial entropy is 0. As time passes, you know less and less about the state of the dice, and entropy increases. You never regain knowledge you have lost unless you make a measurement (which means you don't have a closed system). This is at the heart of the second law.

6. Mar 25, 2016

### Staff: Mentor

From the microscopic point of view, the 2nd law is a combination of the basic statistical fact that the higher the probability of a system being in a state, the more probable it is the system will be found in that state when measured, with the fact that thermodynamic systems are so huge that the probability distribution is extremely narrowly peaked around a given state, to the point that any fluctuation away from that state is too small to measure.

Heat could flow from a cold body to a hot one, but the probability of that happening is so small that in practice, it will never be observed.

7. Mar 25, 2016

### Nathanael

So in this perspective, entropy is a property of an observer? For example, at any moment I could look inside and know the exact state, and hence claim the entropy is zero, but for you the entropy would still be nonzero. So the entropy is "of me" or "of you" and not "of the dice." But in thermodynamics entropy is presented as a state variable, isn't it? The entropy is "of the state of the system" and not "of me" or "of you."

I've yet to really understand entropy; I'm curious how these two perspectives of entropy (informational and thermodynamic) fit together.

8. Mar 25, 2016

### DrStupid

No, it is a property of the system. In statistical thermodynamics the entropy of a macro-state depends on the logarithm of the number of the possible micro-states. In Khashishi's example the initial macro-state is "1" facing up for all dices. As this macro-state has only a single micro-state it's entropy is zero.

9. Mar 25, 2016

### Nathanael

So would you disagree with Khashishi in saying "If you know the initial state exactly, then the initial entropy is 0." ?
In other words, you are saying the entropy is zero because there is only 1 possible configuration which gives all 1s, whereas Khashishi said the entropy is zero because we know exactly what all the dice are.

10. Mar 25, 2016

### DrStupid

He didn't say "because" but "if".

11. Mar 25, 2016

### Nathanael

This quote gives me the impression that it was a more general statement, but perhaps it was meant only for the specific example of all 1s.

At any rate, I appreciate your clarification of entropy as the logarithm of the number of micro states which produce a certain macro state.

12. Mar 25, 2016

### DrStupid

13. Mar 25, 2016

### Staff: Mentor

Irreversibility is the result of (a) viscous dissipation of mechanical energy to internal energy, associated with rapid deformation of a material (b) dissipation of temperature gradients, associated with rapid (spontaneous) conduction of heat in a material, (c) dissipation of concentration gradients, associated with (spontaneous) diffusional transport and mixing of chemical species in a material, and (d) dissipation of chemical potential driving force resulting from (spontaneous) chemical reactions in a system.

14. Mar 26, 2016

### Einstein's Cat

How would one determine such a probability?

15. Mar 27, 2016

### Staff: Mentor

By considering the multiplicity of each macrostate (i.e., the number of microstates associate with each macrostate).

16. Mar 28, 2016

### Khashishi

Actually, when I say "you know it to be in this state", what I mean is that the system is in a pure state. It's not necessary for a conscious observer to exist. When I say, "you don't know the state", what I mean is that the system is in a mixed state*. Presumably, the quantum state of a system is an objective statement, but frankly, we are getting into territory we don't know how to experimentally test, and the answer depends on what interpretation of quantum mechanics you take. (For example, in the many worlds hypothesis, entropy will depend on what apparent "world" you are in.)

When we talk about entropy in classical mechanics and chemistry, we use certain conventions to agree on what the state variables of the system are (i.e. pressure, volume, number of particles, temperature), and we assume the exact position/momentum of every particle is in a heavily mixed state (since it is thoroughly entangled with the surrounding environment). With these conventions, we can talk objectively about the entropy of a classical system.

*a mixed state can be subjective or objective -- the math is the same. It can mean that we don't know the state, so it is in a mix of possibilities, or it can mean that the system is actually entangled with a larger system, so we can't express the complete state of the system within the confines of the smaller system. Macroscopic systems are always entangled with a larger environment, and it is not possible to fully describe the state of any macroscopic system without detailing the state of the entire universe.