scholarly journals Free Energy Density for Gauge Background Fields at Finite Temperature

2011 ◽  
Vol 21 (3) ◽  
pp. 277
Author(s):  
Phan Hong Lien
Keyword(s):  
Free Energy ◽  
Gauge Theory ◽  
Energy Density ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Free Energy Density ◽  
Background Field ◽  
Field Method ◽  
Abelian Gauge ◽  
Background Fields

The effective action and background field method have been applied to investigate free energy density for non-Abelian gauge theory at finite temperature, in which quantum corrections are included and certain symmetries of generating functional are restored. Renormalization is also considered for the gauge field. We give result for the one loop free energy density of gauge theory at high temperature and non-zero chemical potential, correcting a result previously at zero temperature and density. Some results are extended up to two loops

A Thermodynamic-Consistent Model for the Thermo-Chemo-Mechanical Couplings in Amorphous Shape-Memory Polymers

2021 ◽  
pp. 2150022
Author(s):  
Lu Dai ◽  
Rui Xiao
Keyword(s):  
Free Energy ◽  
Energy Density ◽  
Shape Memory ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Shape Memory Polymers ◽  
Free Energy Density ◽  
Entropy Inequality ◽  
Limited Attention ◽  
Solvent Molecules

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

On nematic surface energies

1997 ◽  
Vol 8 (3) ◽  
pp. 293-299 ◽  
Author(s):  
SANDRO FAETTI ◽  
EPIFANIO G. VIRGA
Keyword(s):  
Free Energy ◽  
Liquid Crystal ◽  
Energy Density ◽  
Continuum Theory ◽  
Free Energy Density ◽  
Optic Axis ◽  
Principal Curvatures ◽  
Equilibrium Equations ◽  
Line Integral ◽  
Surface Energies

We review the main outcomes of a continuum theory for the equilibrium of the interface between a nematic liquid crystal and an isotropic environment, in which the surface free energy density bears terms linear in the principal curvatures of the interface. Such geometric contributions to the energy occur together with more conventional elastic contribution, leading to an effective azimuthal anchoring of the optic axis, which breaks the isotropic symmetry of the interface. The theory assumes the interface to be fixed, as for a rigid cavity filled with liquid crystal, and so it does not apply to drops. It should be appropriate when the curvatures of the interface are small compared to that of the molecular interaction sphere. Also, interfaces bearing a sharp edge are encompassed within the theory; a line integral expresses the energy condensed along the edge: we see how it affects the equilibrium equations.

scholarly journals Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

2019 ◽  
Vol 31 (17) ◽  
pp. 175101
Author(s):  
Stiven Villada-Gil ◽  
Viviana Palacio-Betancur ◽  
Julio C Armas-Pérez ◽  
Juan J de Pablo ◽  
Juan P Hernández-Ortiz
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Phase Transitions ◽  
Liquid Crystals ◽  
Energy Density ◽  
Free Energy Density ◽  
Landau Free Energy ◽  
Biaxial Liquid Crystals
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