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

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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,848 answers , 20,603 comments
1,470 users with positive rep
501 active unimported users
More ...

What is the argument for detailed balance in chemistry?

+ 5 like - 0 dislike
31 views

Detailed balance is an important property of many classes of physical systems. It can be written as $$ \frac{p_{i \to j}}{p_{j \to i}} = e^{\frac{\Delta G}{k_B T}},\tag{1} $$ where $i$ and $j$ represent microscopic states of the entire system; $p$ represents the probability for the system to transition from one state to another in a particular finite time period; and $\Delta G$ represents the difference in free energy between the two states. (Whether to use the Gibbs or Helmholtz free energy or some other potential depends on the ensemble.)

Many systems obey detailed balance, but not all do. The Earth cannot fluctuate backwards in its orbit around the Sun, because this would violate conservation of angular momentum. An RLC circuit does not obey detailed balance because the fluctuations have a distinctive ringing time. For these systems the correct formula is $$ \frac{p_{i \to j}}{p_{j' \to i'}} = e^{\frac{\Delta G}{k_B T}},\tag{2} $$ where $i'$ and $j'$ represent states identical to $i$ and $j$, except that all velocities and magnetic fields have been reversed. (In quantum mechanics, they represent something like the complex conjugates of states $i$ and $j$.)

Both of these formulae guarantee that the system will obey the second law (on average), but $(1)$ is substantially stronger, because it guarantees that not only will the system tend toward equilibrium in the thermodynamic limit, but that it will not oscillate as it approaches the equilibrium. (It can still oscillate far away from equilibrium, however.)

My question is about chemical kinetics. Here we universally assume equation $(1)$ and not $(2)$. This puts strong constraints on the reaction rates, and leads to the well-known result that near-equilibrium oscillations are impossible in chemical systems. I've recently been discussing this topic with a very experienced researcher in nonlinear dynamics, and I found myself unable to convince him that $(1)$ rather than $(2)$ is a good assumption in the case of chemistry.

So I thought I'd ask here and see if anyone can help me out: what is the argument that leads us to assume the 'strong' form of detailed balance in chemical systems, rather than the weaker form in equation $(2)$?


This post imported from StackExchange Physics at 2016-02-10 14:15 (UTC), posted by SE-user Nathaniel

asked Jan 18, 2015 in Theoretical Physics by Nathaniel (495 points) [ revision history ]
edited Feb 10, 2016 by Dilaton

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$\hbar$ysicsOv$\varnothing$rflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...