# Thermodynamics as probability rather than unbreakable law?

• mitcho
In summary: So, for example, if you start with a system in a low entropy state and you try to increase the entropy by doing things like breaking things or heating up, then the probability is very small that you will be successful.
mitcho
Excuse me if this is a really ignorant question but I tried searching google but all I got was debunking thermodynamics/creation arguments. My physics lecturer the other day was saying that in third year statistical mechanics we will be shown how to derive a formula giving the probability for the second law of thermodynamics. He said the probability of it being broken was somewhere in range of it happening once in the age of the universe to the power of 100 or something. Does anyone know this exact probability? Also, why is the second law of thermodynamics given such a high esteem as a law. I saw a quote that I can't remember word for word but something like "If you theory opposes Maxwell's equations then all the worse for Maxwell but if it opposes the second law of thermodynamics then all you can do is bow in shame". Any insight would be appreciated.
Thanks.

I'm not an expert on entropy, e.t.c. But I do know that:
The most likely state is the one which can be made by the greatest number of different ways.
For example, if you start off with two separated gases, then remove the partition between them, the most likely outcome is that they will mix. But there is an extremely small probability that they will stay separated.
As another example, if you shuffle a pack of cards, they are most likely to end up in an order with no particular pattern. But there is a very small probability that they will end up in perfect suit and number order.

Clearly, the pack of cards in perfect order is far more likely to happen than the gases staying separate because there are a very large number of gas molecules.
You could work out the exact probability by counting the number of different states which can lead to each possibility.

The second law is indeed only statistical in nature. In particular, the Fluctuation theorem quantifies the probability that one will observe a fluctuation in entropy in the opposite direction that the second law predicts.

First of all, it is not an ignorant question at all. In fact, it is a very valid and important question to ask. The idea of thermodynamics as a probability rather than an unbreakable law is a topic of ongoing debate and research in the scientific community. It is known as the "fluctuation theorem" and it suggests that the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time, is actually a statistical average rather than an absolute rule.

In other words, while the second law of thermodynamics holds true on a macroscopic scale, there is a small possibility that it can be violated on a microscopic scale due to random fluctuations. This is where the concept of probability comes into play - the second law is still highly probable to hold true, but it is not an absolute certainty.

As for the exact probability of the second law being broken, it is difficult to determine as it depends on various factors such as the size and complexity of the system, the duration of observation, and the accuracy of measurements. However, studies have shown that the probability is extremely low, on the order of 1 in 10^100, which is a number so small that it is practically impossible to occur.

The second law of thermodynamics is given high esteem as a law because it has been extensively tested and observed in various physical systems. It has also been mathematically proven using statistical mechanics, which is why your lecturer mentioned it in your third-year course. It is a fundamental principle in understanding the behavior of energy and matter in our universe and has wide applications in fields such as engineering, chemistry, and biology.

In conclusion, while the idea of thermodynamics as a probability rather than an absolute law is still being researched and debated, the second law remains a crucial and highly reliable principle in our understanding of the physical world. It is important to continue questioning and exploring these concepts, but we must also acknowledge and respect the established laws and theories that have been supported by extensive evidence and experimentation.

## What is thermodynamics as probability?

Thermodynamics as probability is a concept in physics that views the laws of thermodynamics as statistical laws rather than unbreakable physical laws. It suggests that the behavior of large systems can be explained and predicted by looking at the probabilities of individual particles within the system.

## How does thermodynamics as probability differ from traditional thermodynamics?

In traditional thermodynamics, the laws are seen as absolute and unbreakable, with no room for randomness or probability. However, thermodynamics as probability takes into account the unpredictable nature of particles and their interactions, and views the laws as statistical rather than absolute.

## What evidence supports the idea of thermodynamics as probability?

One of the main pieces of evidence for thermodynamics as probability is the behavior of large systems, such as gases and liquids, which can be accurately predicted using statistical methods. Additionally, quantum mechanics has shown that at the atomic level, particles do not always behave in a predictable manner, further supporting the idea of probability in thermodynamics.

## What are the implications of viewing thermodynamics as probability?

Viewing thermodynamics as probability has significant implications for our understanding of the universe and the laws that govern it. It suggests that there is a level of randomness and unpredictability in the behavior of particles, and that the laws of thermodynamics are not as absolute as previously thought.

## How does thermodynamics as probability impact current scientific research?

Thermodynamics as probability has influenced many areas of scientific research, such as materials science, chemistry, and biology. It has led to a deeper understanding of how systems behave and has opened up new avenues for studying and predicting the behavior of complex systems. It has also influenced the development of new technologies and materials.

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