The meaning of temperature in nano particles

[saray1360]

Hi,

I always had the idea that temperature is a thermodynamical property which means that the statistical number of particles are important in measuring the relative temperature of the system.

But, what happens when it comes to nano particles in which we have low numbers of atoms. How temperature is described then?

Regards,

 

[alxm]

To quote an old prof of Atomic & Molecular Physics I know: "Temperature is something you measure with a thermometer."

The smaller the statistical ensemble you've got, the less meaningful it is.

 

[Naty1]

You can get some further insights here:

http://en.wikipedia.org/wiki/Temperature#Theoretical_foundation

which discusses the theoretical temperature of the vacuum and an entropy interpretation of temperature...but the relationship between these, and also information for that matter, is not at all clear to me...in fact, I am unsure anyone really understands entropy to this day...

 

[sokrates]

Temperature might lose its meaning , but there's still a sound microscopic understanding of "heat".

And even in nano-electronic devices, or thermo-electric devices I cannot think of an example where the number of "electrons" or "atoms" involved defying the concept of temperature.

I don't think this is a practical issue. It's just academic

 

[jensa]

Hi,

I always had the idea that temperature is a thermodynamical property which means that the statistical number of particles are important in measuring the relative temperature of the system.

But, what happens when it comes to nano particles in which we have low numbers of atoms. How temperature is described then?

Regards,

As far as I know, it is not meaningful to talk about temperature of an isolated system of very few degrees of freedom. However, in reality all such systems are (to some extent) coupled to an environment which has many degrees of freedom. This coupling will eventually lead to a statistical distribution for the small system with a temperature defined by the temperature of the bath (environment). The time scale at which this happens depends on the coupling (interaction) between the system and the bath.

EDIT:
I think Brownian motion is a good classical example. Here we are talking about a heavy particle interacting with bunch of lighter particles (forming an environment or bath). If the heavy particle were isolated it would not make any sense to ask "What is the temperature?". However, due to the interaction with the environment which can be described by random kicks (stochastic force) the properties of the particle (velocity and position) become randomized with a statistical distribution which after long enough time becomes the Boltzmann distribution with temperature of the bath.

A quantum example would be a two-level system (qubit) interacting with the environment to "obtain a temperature".