Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Is it possible to define a notion of temperature in a microcanonical ensemble?

+ 1 like - 0 dislike
1311 views

I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this?

Can I think of temperature of this system as the average kinetic energy for all the particles?


To put the thing in a larger context - what is the implicit choice of ensemble when people define the entropy of a black-hole either as (1) horizon area or (2) via microstate counting or (3) macroscopically via quantum entropy function ?

Naively it feels that for a black-hole entropy one must think of a microcanonical ensemble because its not clear to me as to with what "bath" will it be able to exchange anything to maintain any chemical potentials for the conserved charges, volume or energy...may be I am being too naive...

This post imported from StackExchange Physics at 2014-04-14 17:03 (UCT), posted by SE-user user6818
asked Apr 13, 2014 in Theoretical Physics by user6818 (960 points) [ no revision ]
What about the standard definition of temperature for a microcanonical ensemble (appearing in every textbook on statistical mechanics) $\frac{1}{T} = \frac{\partial S}{\partial E}$? Where $S$ is the entropy of the system and $E$ its energy.

This post imported from StackExchange Physics at 2014-04-14 17:03 (UCT), posted by SE-user V. Moretti

1 Answer

+ 1 like - 0 dislike

In a microcanonical system, one defines the entropy $S$ as $k$ times the logarithm of the microcanonical partition function (depending on energy $E$, particle number $N$, and volume $V$) and the temperature $T$ as $[(dS/dE)_{N,V}]^{-1}$. See, e.g., 

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.73.2875

However, in order that thermodynamical variables satisfy the usual thermodynamic relations (and hence have the usual meaning!), one must take the thermodynamic limit of infinitely many particles. For finite systems, these relations are only approximately valid. 

answered Apr 14, 2014 by Arnold Neumaier (15,787 points) [ revision history ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverf$\varnothing$ow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...