Download Thermodynamic Self-Consistency and Deconfinement

Thermodynamic SelfConsistency and
Deconfinement Transition
Zheng 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 transition
as follows
Local charge neutrality
Character: constant-pressure
The total energy and baryon number densities of mixed
phase
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 chemical
potentials
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 mixed
phase
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-dependent
parameter (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
(I)
For conserved baryon number, Y is respectively
If two phases are in chemical equilibrium,
the equation becomes
(II)
and
,
However, the situation will be different if phase transition
is in progress. We find
changes with increasing density.
Because
an extra
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)
By the following treatment
partial
derivative
acquirement of zero point energy
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.
Substitute
into the equation (III) or equation (I),
we obtain the following formula
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
Whether the two derivatives equal each other
determines whether two phases are in chemical equilibrium
or not.
Equilibrium and nonequilibrium
deconfinement transitions
Traditional transition (constant-pressure case)
Two phases in mixed phase are always in chemical
equilibrium
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 released
when the density increases from this equation.
If the compact star spins down, the deconfinement takes
place and then the energy is released.
We can calculate the total heat through the mixed phase
region at a given time
If the baryon number N is
,
the heat luminosity is roughly estimated as
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 effect
What is its microphysics?( Maybe nonlinear physics can tell
us something)
Thank you