Can a single particle be in equilibrium ?

[jfitz]

Can a single particle be in "equilibrium"?

If a single particle is in a double potential well (with different depths), is it correct to say it is in "equilibrium" in the statistical mechanics sense of the word? The particle will bounce back and forth and be in each well with some probability which is independent of time, but it's unclear to me whether this is equilibrium or non-equilibrium steady state.

What if there were many particles in the system with the same double well... would that change the answer?

 

[LightHero]

Yes, a single particle can be in an equilibrium state. This is because equilibrium is defined as a state where the particle's probability distribution remains constant over time. In a double potential well, the particle will be in each well with some probability which does not change over time, thus meeting the definition of an equilibrium state. If there are many particles in the system with the same double well, then the answer would remain the same. All of the particles would still be in equilibrium, as their probability distributions would remain constant over time.

 

[sir-pinski]

In the context of statistical mechanics, equilibrium refers to a state in which there is no net flow of energy or particles between different parts of a system. This means that the system is in a steady state and all macroscopic properties such as temperature, pressure, and concentration are constant.

In the case of a single particle in a double potential well, it is not considered to be in equilibrium as it is still undergoing constant motion and there is a net flow of energy between the two wells. This can be seen by the fact that the particle is able to move back and forth between the wells with some probability, indicating that there is still a non-equilibrium state present.

However, if there were many particles in the system with the same double well, the answer may change. In this case, the system may reach a state of statistical equilibrium where the net flow of energy between the wells becomes negligible and the particles are distributed evenly between the two wells. This can be thought of as a non-equilibrium steady state, where the system is not in equilibrium but is in a steady state with constant macroscopic properties.

In conclusion, a single particle in a double potential well is not considered to be in equilibrium in the statistical mechanics sense of the word. However, if there are many particles present, the system may reach a state of non-equilibrium steady state. It is important to note that the concept of equilibrium is only applicable in the macroscopic scale and may not hold true for individual particles in a system.