Thermodynamic Self-Consistency and

Deconfinement TransitionZheng Xiaoping

Beijing 2009

• 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

Phase transition

with two conserved charges

The standard scenario for first-order phase transitionas follows

Character: constant-pressure

Local charge neutrality

The total energy and baryon number densities of mixedphase

where are independent of

Glendenning(1992, PRD, 46,1274) gave a construction method for the system having two conserved charges (electric charge, baryon number)

2 chemicalpotentials

Global charge neutrality

or

Phase transition takes place in a region of pressure

Schertler et al, 2000, Nucl.Phys.A677:463-490

The total energy and baryon number densities of mixedphase

The densities are nonlinear function of

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-dependentparameter (here replaced by ), we have thermodynamic self-consistency problem( Gorenstein and Yang, 1995, PRD, 52,5206)

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)

However, the situation will be different if phase transitionis in progress. We find changes with increasing density.Because

the equation (II) is not satisfied self-consistently. To maintain the thermodynamic self-consistency, we mustadd a “zero point energy” to the system. i.e.,

We rewrite equation (II) as( replace e by e*)

(III)

an extra

By the following treatment

Equation (III) is self-consistent. Since the differenceof 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

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 equilibriumor not.

On the left-hand side, it means change in chemical energy for a conversionThe right-hand side implies a departure of the system from the equi-state

Equilibrium and nonequilibrium deconfinement transitions

Traditional transition (constant-pressure case)

Two phases in mixed phase are always in chemicalequilibrium

The phase transition presented by Glendenning

The two phases are not quite in chemical equilibrium during phase transition

Application: Heat Generation

We find that the chemical energy would be releasedwhen the density increases from this equation.

If the compact star spins down, the deconfinement takesplace and then the energy is released.

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.

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 effectWhat is its microphysics?( Maybe nonlinear physics can tell us something)

Thank you