Distance between equilibrium and nonequilibrium states

[Billy Yang]

Recently, the properties of nonequilibrium many-body quantum systems have aroused great curiosity of physicists. Numerous papers have been published about this area. But how do we measure how far the system is from equilibrium states?

There are several proposals have been published, for example, using the heat which has been negated or using diagonal entropy. I am wondering whether using diagonal entropy to measure nonequilibrium has some flaws.

In thermodynamics, is there a measure to describe the distance between equilibrium and nonequilibrium?

Thanks so much!

 

[atyy]

I googled "diagonal entropy", and these came up which look interesting.

http://online.kitp.ucsb.edu/online/qdynamics12/santos/pdf/Santos_QDynamics12_KITP.pdf

http://arxiv.org/abs/1202.4764
Weak and strong typicality in quantum systems
Lea F. Santos, Anatoli Polkovnikov, Marcos Rigol
Phys. Rev. E 86, 010102(R) (2012)

 

[Billy Yang]

Thanks for your response. After carefully viewing this paper, I found the hypothesis in this paper is interesting. Thanks again.

 

[atyy]

These papers use the trace norm of the difference between the density operator and the density operator representing thermal equilibrium.

http://arxiv.org/abs/quant-ph/0511225
http://arxiv.org/abs/1008.4162
http://arxiv.org/abs/1004.1843

 

[Billy Yang]

:-) Good papers. Do you think the term equilibrium for a quantum system is weird? In Rigol's paper, PRL, 98, 050405, the measure for a quantum system to reach equilibrium is whether the momentum distribution becomes averaged.