Are the Fundamental Assumptions of Non-Equilibrium Thermodynamics Founded?

Dear Colleagues,

Entropy as a state function is defined only for equilibrium states. It can also be applied to systems which are not far from equilibrium. For such systems, the assumption of “local equilibrium” is justified. The idea is that the entire system may be divided into macroscopic subsystems, each of which one can assume is a local equilibrium.

For systems which are very far from equilibrium, there are some difficulties in extending the definition of entropy and the application of the Second Law of Thermodynamics.

The main points which we open for discussion in this Special Issue are the following:

1. Can one justify the assumption of “local equilibrium” for systems far from equilibrium?

2. Can one define an “entropy density?”

This means a quantity s, such that for any element of volume, dV, and a point R, the quantity s(R)dV is the entropy of that element of volume.

3. Can one justify the assumption that the local density s(e,v,n) has the same functional dependence on the local energy (e), local volume (ν), and local number of particles n as the function S(E,V,N) for a macroscopic system at equilibrium?

4. Can one justify the integration of the entropy density s(R) over the entire volume V to obtain the entropy of the system?

S=∫s(R)dV

5. Can one define a “local entropy production” , such that the total entropy production in the entire macroscopic system is:

(d_iS)/dt=∫σdV ?

Most textbooks on non-equilibrium thermodynamics make these assumptions without any justification. In this issue, we invite experts on thermodynamics to provide either justification or criticism of these assumptions.

Prof. Dr. Arieh Ben-Naim
Guest Editor

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