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Thermodynamic Self-Consistency and
Deconfinement TransitionZheng Xiaoping
Beijing 2009
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• 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
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Phase transition
with two conserved charges
The standard scenario for first-order phase transitionas follows
Character: constant-pressure
Local charge neutrality
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The total energy and baryon number densities of mixedphase
where are independent of
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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
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Phase transition takes place in a region of pressure
Schertler et al, 2000, Nucl.Phys.A677:463-490
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The total energy and baryon number densities of mixedphase
The densities are nonlinear function of
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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)
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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)
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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
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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
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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
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Equilibrium and nonequilibrium deconfinement transitions
Traditional transition (constant-pressure case)
Two phases in mixed phase are always in chemicalequilibrium
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The phase transition presented by Glendenning
The two phases are not quite in chemical equilibrium during phase transition
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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.
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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.
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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)
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Thank you