1. Thermodynamic Self- Consistency and Deconfinement Transition Zheng Xiaoping Beijing 2009

2. Phase transition with two conserved charges(to compare two kinds of phase transition) Thermodynamics during phase transition (realize the self-consistency of thermodynamics) Equilibrium and nonequilibrium deconfinement transitions Possible application and a summary

3. Phase transition with two conserved charges The standard scenario for first-order phase transition as follows Character: constant-pressure Local charge neutrality

4. The total energy and baryon number densities of mixed phase where are independent of

5. Glendenning(1992, PRD, 46,1274) gave a construction method for the system having two conserved charges (electric charge, baryon number) 2 chemical potentials Global charge neutrality or

6. Phase transition takes place in a region of pressure Schertler et al, 2000, Nucl.Phys.A677:463-490

7. The total energy and baryon number densities of mixed phase The densities are nonlinear function of

8. Thermodynamics during phase transition We introduce a parameter, baryon number fraction for convenience. And then energy per baryon in mixed phase is expressed as Of course, the energy is the function of form If the energy of a system is with a -dependent/T-dependent parameter (here replaced by ), we have thermodynamic self-consistency problem ( Gorenstein and Yang, 1995, PRD, 52,5206)

9. We now write the fundamental thermodynamic equation for the coexistence of two phases as For conserved baryon number, Y is respectively and If two phases are in chemical equilibrium,, the equation becomes (I) (II)

10. However, the situation will be different if phase transition is in progress. We find changes with increasing density. Because the equation (II) is not satisfied self-consistently. To maintain the thermodynamic self-consistency, we must add a “zero point energy” to the system. i.e., We rewrite equation (II) as( replace e by e*) (III) an extra

11. By the following treatment Equation (III) is self-consistent. Since the difference of chemical potentials between two phases is The equation (III) go back to the equation (I) The term can be nonzero. partial derivative acquirement of zero point energy

12. Substitute into the equation (III) or equation (I), we obtain the following formula Whether the two derivatives equal each other determines whether two phases are in chemical equilibrium or not. On the left-hand side, it means change in chemical energy for a conversion The right-hand side implies a departure of the system from the equi-state

13. Equilibrium and nonequilibrium deconfinement transitions Traditional transition (constant-pressure case) Two phases in mixed phase are always in chemical equilibrium

14. The phase transition presented by Glendenning The two phases are not quite in chemical equilibrium during phase transition

15. Application: Heat Generation We find that the chemical energy would be released when the density increases from this equation. If the compact star spins down, the deconfinement takes place and then the energy is released.

16. If the baryon number N is, the heat luminosity is roughly estimated as We can calculate the total heat through the mixed phase region at a given time This is compatible with neutrino emission. It will significantly influence the thermal evolution of the compact stars.

17. Summary Two phases are imbalance during deconfinement phase transition which is presented by Glendenning (This is the requirement of self-consistent thermodynamics) The released chemical energy will significantly influences neutron star cooling The energy release is the thermodynamic effect What is its microphysics?( Maybe nonlinear physics can tell us something)

18. Thank you