# Thermodynamic equipartition of energy theorem - application to life

• trelek2
In summary, the conversation discusses simulating a system of molecules, specifically water, and the energy barrier they need to overcome to pass through a barrier. The speaker also mentions the probability of a water molecule passing the barrier and the average energy of a water molecule at 320K. They also ask about the degrees of freedom for water molecules and the average energy of ions in the system. The speaker suggests considering pressure and the Maxwell-Boltzman Distribution for a rough estimate.
trelek2
hi, I'm simulating a system of molecules (water) and in order to pass through a barrier they have to overcome an energy barrier of 4kT. What is the probability of a water molecule passing the barrier or perhaps what is the average energy of a water molecule in my system?

I know it's 1/2 *kT per each degree of freedom, but how many degrees of freedom do my water molecules have? (I'm simulating at 320K, water molecules are SPC/E).

Oh, and i also have ions in my system. What is their average energy? 3/2kT?

Thanks for any insight!

Did you mean degrees of freedom per water molecule?

http://www.pha.jhu.edu/~broholm/l37/node5.html

Perhaps you should also take into consideration the pressure and pressure difference in the water?

Last edited by a moderator:
It's not that trivial for fluids due to interactions. You can basically look at Maxwell-Boltzman Distribution which deals with something very similar for gases, and you might be able to use it as a rough estimate for water, but don't expect anything particularly good out of it.

## 1. What is the thermodynamic equipartition of energy theorem?

The thermodynamic equipartition of energy theorem states that, at thermal equilibrium, the total energy of a system is equally distributed among all of its degrees of freedom. This means that each degree of freedom, such as the translational, rotational, and vibrational energies of molecules, will have an equal amount of energy on average.

## 2. How is the thermodynamic equipartition of energy theorem applied to life?

In living systems, the thermodynamic equipartition of energy theorem helps to explain how energy is distributed and utilized. For example, in biological processes such as metabolism and photosynthesis, energy is transferred and distributed among different molecules and structures in a way that is consistent with this theorem.

## 3. What is the significance of the thermodynamic equipartition of energy theorem in understanding life?

The thermodynamic equipartition of energy theorem helps to explain the efficient use and transfer of energy in living systems. It also provides a framework for understanding the relationship between energy and entropy, and how living organisms are able to maintain a state of low entropy, or high organization, despite the constant increase in entropy of the universe.

## 4. Are there any exceptions to the thermodynamic equipartition of energy theorem in living systems?

While the thermodynamic equipartition of energy theorem generally holds true in living systems, there are some exceptions. For example, in certain biological processes, such as enzyme-catalyzed reactions, specific molecules may have a higher concentration of energy than others, deviating from the equal distribution predicted by the theorem.

## 5. How does the thermodynamic equipartition of energy theorem relate to the second law of thermodynamics?

The thermodynamic equipartition of energy theorem is a direct consequence of the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. The theorem provides a more specific understanding of how energy is distributed and utilized in accordance with the second law.

• Thermodynamics
Replies
1
Views
1K
• Thermodynamics
Replies
13
Views
1K
• Thermodynamics
Replies
3
Views
977
• Thermodynamics
Replies
7
Views
1K
• Thermodynamics
Replies
4
Views
2K
• Thermodynamics
Replies
13
Views
2K
• Thermodynamics
Replies
5
Views
949
• Thermodynamics
Replies
1
Views
2K
• Thermodynamics
Replies
6
Views
1K
• Thermodynamics
Replies
1
Views
2K