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.

Quantum Mechanical Ensemble Averages and Statistical Thermodynamics

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Free Energy ◽  
Thermal Energy ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Quantum Statistical Mechanics ◽  
Bose Condensation ◽  
Distribution Functions ◽  
Ensemble Average ◽  
Statistical Thermodynamic ◽  
Quantum Mechanical

Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

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.

Solar Thermal Energy

2018 ◽  
Author(s):  
E. L. Wolf
Keyword(s):  
Solar Cells ◽  
Thermal Energy ◽  
Fossil Fuel ◽  
Rankine Cycle ◽  
Carnot Cycle ◽  
The Sun ◽  
Solar Thermal Energy ◽  
Heat Engines ◽  
Direct Use ◽  
Fossil Fuel Energy

The Sun’s spectrum on Earth is modified by the atmosphere, and is harvested either by generating heat for direct use or for running heat engines, or by quantum absorption in solar cells, to be discussed later. Focusing of sunlight requires tracking of the Sun and is defeated on cloudy days. Heat engines have efficiency limits similar to the Carnot cycle limit. The steam turbine follows the Rankine cycle and is well developed in technology, optimally using a re-heat cycle of higher efficiency. Having learned quite a bit about how the Sun’s energy is created, and how that process might be reproduced on Earth, we turn now to methods for harvesting the energy from the Sun as a sustainable replacement for fossil fuel 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.

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.

Experimental evidence for the need of thermodynamic considerations in modelling of anaerobic environmental bioprocesses

1997 ◽  
Vol 36 (10) ◽  
pp. 109-115 ◽  
Author(s):  
Choon-Yee Hoh ◽  
Ralf Cord-Ruwisch
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Positive Reaction ◽  
Rate Equation ◽  
Dynamic Equilibrium ◽  
Reaction Rates ◽  
Product Inhibition ◽  
Experimental Results ◽  
Biological Processes ◽  
Laws Of Thermodynamics

For modeling of biological processes that operate close to the dynamic equilibrium (eg. anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached dynamic equilibrium. Traditional Michaelis-Menten based models were found to violate the laws of thermodynamics as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. The inclusion of empirical “product inhibition factors” as suggested by previous work could not prevent this problem. This paper compares the predictions of the Michaelis-Menten Model (with and without product inhibition factors) and the Equilibrium Based Model (which has a thermodynamic term introduced into its rate equation) with experimental results of reactions in anaerobic bacterial environments. In contrast to the Michaelis-Menten based models that used traditional inhibition factors, the Equilibrium Based Model correctly predicted the nature and the degree of inhibition due to endproduct accumulation. Moreover, this model also correctly predicted when reaction rates must be zero due to the free energy change of the conversion reaction being zero. With these added advantages, the Equilibrium Based Model thus seemed to provide a scientifically correct and more realistic basis for a variety of models that describe anaerobic biosystems.

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.

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