Helmholtz Free Energy for Certain Negatively Curved Space-Times, and the Selberg Trace Formula

2003 ◽  
pp. 321-332
Author(s):  
Floyd Williams
Keyword(s):  
Free Energy ◽  
Trace Formula ◽  
Helmholtz Free Energy ◽  
Selberg Trace Formula ◽  
Curved Space ◽  
Negatively Curved

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

scholarly journals A Selberg trace formula for hypercomplex analytic cusp forms

2015 ◽  
Vol 148 ◽  
pp. 398-428 ◽  
Author(s):  
D. Grob ◽  
R.S. Kraußhar
Keyword(s):  
Trace Formula ◽  
Cusp Forms ◽  
Selberg Trace Formula

Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

2015 ◽  
Vol 233-234 ◽  
pp. 331-334
Author(s):  
Anna Yu. Solovyova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Free Energy ◽  
External Magnetic Field ◽  
Volume Concentration ◽  
Helmholtz Free Energy ◽  
Hard Spheres ◽  
Particle Volume ◽  
Simulation Data ◽  
Theoretical Predictions

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

scholarly journals Hamiltonian Thermodynamics

2020 ◽  
Vol 16 (4) ◽  
pp. 557-580
Author(s):  
S.A. Rashkovskiy ◽  
Keyword(s):  
Free Energy ◽  
Hamiltonian Systems ◽  
Thermal Energy ◽  
Helmholtz Free Energy ◽  
Random Processes ◽  
Carnot Cycle ◽  
Thermodynamic Process ◽  
Thermodynamic Cycles ◽  
Thermodynamic State ◽  
Laws Of Thermodynamics

It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.

scholarly journals SEIBERG–WITTEN PREPOTENTIAL FROM WZNW CONFORMAL BLOCK: LANGLANDS DUALITY AND SELBERG TRACE FORMULA

2012 ◽  
Vol 27 (22) ◽  
pp. 1250129
Author(s):  
TA-SHENG TAI
Keyword(s):  
Trace Formula ◽  
Conformal Block ◽  
Selberg Trace Formula ◽  
Conformal Blocks ◽  
Langlands Duality

We show how SU(2) Nf = 4 Seiberg–Witten prepotentials are derived from [Formula: see text] four-point conformal blocks via considering Langlands duality.

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