The Arrow of Time: Entropy & System Evolution

[paco1955]

it is the change in entropy that ultimately provides us with the answer to why systems will naturally evolve in one direction with time and not the other: systems always evolve in time in such a way that the total entropy of system + environment increases. If you observe a system in which the entropy appears to decrease, you can be sure that somewhere there is a change in the entropy of the environment large enough to make the total entropy change positive. for example, suppose that in a closed system i drop an ice cube in a container full of hot water. heat will flow from the hot water to the ice. the temperature of the hot water drops and the ice melts simultaneously until both bodies of water reach the same temperature and form a homogeneous luke-warm body of water. the cooling process of the hot water is a negative entropy change. in other words, the entropy of the hot water decreases. (the hot water changes from a relatively disorganized state to a more organized state.) the melting process of the ice is a positive entropy change. in other words, the entropy of the ice increases. (the ice changes from a relatively organized state to a more disorganized state.) it turns out that the positive entropy change of the ice is greater than the negative entropy change of the hot water. in other words, if you observe the hot water in which the entropy appears to decrease, you can be sure that there is a change in the entropy of the ice large enough to make the total entropy change positive. if "sh" is the negative entropy change of the hot water (sh < 0) and "si" is the positive entropy change of the ice (si > 0), then sh + si > 0.

 

[Greg Bernhardt]

That makes a lot of sense! So basically, the total entropy of the system and environment always increases, even if the entropy of one part of the system (like the hot water in this example) appears to decrease. This is because the entropy change in the other part of the system (like the ice in this example) is greater than the entropy change in the first part. Thank you for explaining this concept so clearly!

 

[GSXR750]

This content highlights the concept of entropy and its role in the arrow of time and system evolution. Entropy is a measure of the disorder or randomness in a system, and it tends to increase over time. This means that systems will naturally evolve in a way that increases their overall entropy.

The example of dropping an ice cube into hot water illustrates this concept. The hot water cools down and the ice melts, both processes leading to a decrease in entropy. However, the increase in entropy of the melted ice is greater than the decrease in entropy of the hot water, resulting in a net increase in entropy. This is why systems always evolve in a way that increases the total entropy of the system and its surroundings.

This understanding of entropy and its relationship to the arrow of time is crucial in many fields, from thermodynamics to cosmology. It helps us understand why certain processes are irreversible and why time only moves forward. The increase in entropy is a fundamental principle that governs the behavior of systems and plays a key role in our understanding of the world around us.

In conclusion, the concept of entropy is essential in explaining the arrow of time and the evolution of systems. It provides us with a deeper understanding of the natural processes that occur in our universe and allows us to make predictions about the future behavior of systems.