# Does the entropy of a closed system always increase

#### Jeebus

Question: Does the entropy of a closed system always increase, or could it possibly decrease?

Answer: The standard answer to your question from the laws of thermodynamics is that entropy (disorder) will increase, but there are at least two ways I believe entropy can decrease in a closed system.

First, you used the word 'possibly'. The laws of probability allow a closed system's entropy to decrease, but with such a low likelihood that the odds would make it very unlikely. Making the system small enough, however, by decreasing the number of its possible states can help improve the odds.

Take, for example, a movie of a billiards game 'break' shot. The ordered arrangement of balls becomes disordered, but running the film in reverse would show each individual collision obeying the usual physical laws. The time reversal would be apparent, however, when all the balls ended up in an ordered collection. Although that result could conceivably occur by chance, it is very unlikely. Reducing the example to just two balls would make the odds of an orderly arrangement occurring more likely.

For a second example of decreasing entropy, start with a closed system large enough to allow significant gravitational forces among its components. Gravity provides a 'negative energy' that can take a completely disordered system and organize it into a radically symmetric arrangement around a common center of gravity.

Follow-up Question to above Answer: Regarding the above example of the 2nd law and gravity "organizing" the balls...In that case, wouldn't the balls be in a non-equilibrium state to begin with, since it allows for seemingly automatic movement of the balls? That would mean that not all the conditions for 2LOT have been fulfilled and it would not be a great surprise to see some end-state of organization, right?

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#### jcsd

Gold Member
You are right staiscally it is possible in any closed system for entropy to increase, indeed on very small scales, over short time periods this has been observed. Note the second law really should say 'tend' to increase rather than 'will' increase' at is a staistcal process.

Gravity is no way to combat entropy, your forgetting the GPE lost by objects as the fall towards mass.

#### russ_watters

Mentor
So first one is right, second is wrong. But hey, that first one was pretty darn good - its essentially a logical proof of the Heisenberg Uncertainty Principle.

#### Njorl

Thermodynamics is a subset of the field Statistical Mechanics. It is implicit in the field that sample sizes will be sufficiently large to essentially disregard that which is statistically insignificant. By applying the 2nd law of thermodynamics, a large enough sample size is assumed to make it true. Otherwise, you really have a "many-body" problem, in which you must solve for each individual body's state.

Njorl

#### Jeebus

Originally posted by Njorl
Thermodynamics is a subset of the field Statistical Mechanics. It is implicit in the field that sample sizes will be sufficiently large to essentially disregard that which is statistically insignificant. By applying the 2nd law of thermodynamics, a large enough sample size is assumed to make it true. Otherwise, you really have a "many-body" problem, in which you must solve for each individual body's state.

Njorl

Ok. Thanks for the insight.

"Does the entropy of a closed system always increase"

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