Gibbs Distribution in Canonical Ensemble: Explaining Physical Principles

[quantumfireball]

In canonical ensemble all energy values are permitted.
The distribution of energies of system at temp T follows Gibbs Distribution.
My question is simple.
Why is it that all energies are permitted??
forget the mathematical derivation.
How to understand it physically.
Does it not take the same amount of heat for all the copies of the system (in their respectable thermal baths) to raise their temperature,so that equilibrium is achieved with the heat bath.
Why do some absorb more heat and some less to attain equilibrium?


I am sure that these questions that i ask seem very immature to most of youll guys.
But since i am not from physics or chemistry background i have lot of 'knowledge loopholes'

 

[Valerie Park]

which i am trying to fill up.I understand that the Gibbs Distribution is a probabilistic approach in calculating the energies of the system. But still why is it that all energies are permitted? The answer to your question is that the canonical ensemble is based on the principle of maximum entropy. This means that the system is allowed to explore all possible energy states, and the probability of each energy state is determined by the entropy of the system. In other words, the system is allowed to fluctuate between different energy states, and the probability of each state is determined by the entropy of the system. In essence, all energy states are permitted, as long as the overall entropy of the system is maximized.

 

[charng]

to fill.

The concept of Gibbs distribution in the canonical ensemble is based on the principle of energy exchange within a closed system. In this ensemble, the system is in thermal equilibrium with a heat bath at a constant temperature. This means that the system and the heat bath are in a state of balance, with no net transfer of energy between them.

In this scenario, all energy values are permitted because the system is able to exchange energy with the heat bath in an unrestricted manner. This is due to the fact that the system and the heat bath are in thermal contact, allowing for the exchange of energy through processes such as heat transfer or chemical reactions.

The Gibbs distribution describes the probability of finding the system in a particular energy state at a given temperature. It is based on the Boltzmann factor, which takes into account the energy of the system and the temperature of the heat bath. This distribution shows that at higher temperatures, there is a higher probability of finding the system in a higher energy state, and at lower temperatures, there is a higher probability of finding the system in a lower energy state.

To understand this concept physically, we can think of the system as a collection of particles that are constantly moving and interacting with each other. At a higher temperature, the particles have more energy and are moving faster, increasing the chances of them occupying higher energy states. At a lower temperature, the particles have less energy and are moving slower, making it more likely for them to occupy lower energy states.

In terms of heat exchange, it is important to note that the amount of heat required to raise the temperature of a system is dependent on its specific heat capacity. This means that different systems may require different amounts of heat to reach the same temperature. This is why some systems may absorb more heat and some may absorb less to reach equilibrium with the heat bath.

I hope this explanation helps to fill in some of the knowledge gaps you mentioned. It is always important to ask questions and seek understanding, no matter what background you come from. Keep learning and exploring!