Entropy current

This definition suggests a reasonable formulation of entropy current density as... 

The entropy is given in terms of the specific entropy shy S = J pscPr so that the entropy flux out of the system is related to the entropy current density by... 

The entropy change with the environment involves energy flow. / and the flows of S and P, and the entropy current is... 

Fig. 3.18 Entropy current through a wall. The resistance which the wall imposes to the flux depends upon the thickness d, the area A through which the entropy flows, and the conductivity of the material.

Coupling of Matter and Entropy Currents What happens when a substance is simultaneously subjected to a gradient of its potential p and the temperature T Let us imagine a pond where the water below is cold, Ti, and heats up in the Sun becoming warm above with 7 2 > Tj. Then y 2 = + ( 2 — Ti) < would be... 

The balance equation for entropy can be derived using the conservation of energy and the balance equation for the concentrations. This gives us an explicit expression for entropy production or— which can be related to irreversible processes such as heat conduction, diffusion and chemical reactions—and the entropy current is- The formal entropy balance equation is... 

As was the case for the energy current, the expression for the entropy current consists of two parts, one due to heat flow and the other due to matter flow. 

Figure 17.1 A simple thermal gradient maintained by a constant flow of heat. In the stationary state, the entropy current Js,out — diS/dt + The stationary state can be obtained either as a solution of the Fourier equation for heat conduction or by using the theorem of minimum entropy production. Both lead to a temperature T(x) that is a linear function of the position x...

In the above, Ps(r, t) is the entropy density, Osir, t) the entropy source strength, and Jsip, t) the entropy current density. The volmne integrations in Eqs. (293) (294b) are over the spatial domain V occupied by the system. The surface integration in Eq. (295) is over the boundary surface S separating the system from its surroundings. The unit vector h is normal to S and directed outward. 

Ni-doped Cu2ZnSnS4 nanocrystals, two new different lines at g = 2.23 and g = 2.06 are observed, which are attributed to the Ni " electron spin [34]. Most important is that the EPR line of Ni " becomes stronger with temperature increasing to 570 K, which indicates the stronger entropy current derived from the electron spin of Ni " and then results in the enhanced thermopower in Ni-doped Cu2ZnSnS4 nanocrystals. 

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