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NEGF Method for Design and Simulation Analysis of Nanoscale MOS Devices
Published in Ashish Raman, Deep Shekhar, Naveen Kumar, Sub-Micron Semiconductor Devices, 2022
A system like a molecule that consists of a large number of discrete particles whose energies and physical state constantly change with time needs a large number of variables to describe the system's state. It does this by using microscopic thermodynamics. A macrostate represents the collective behavior of a system, whereas a microstate describes the entire system in terms of physical quantities of discrete particles. The total number of a microstate is a function of energy E, several particles N, and volume V and is denoted by W(N, V, E) [29]. The thermodynamic properties of any given system can be determined by function W(N, V, E). Figure 12.5 shows the energy, particles, and volume exchange of two systems that are brought into contact.
Chemical Thermodynamics and Thermochemistry
Published in Armen S. Casparian, Gergely Sirokman, Ann O. Omollo, Rapid Review of Chemistry for the Life Sciences and Engineering, 2021
Armen S. Casparian, Gergely Sirokman, Ann O. Omollo
As a second component of thermodynamics, entropy is a measure of the statistical disorder or randomness of a system. The universe tends to move toward greater total disorder, and this is expressed in terms of entropy or S. Entropy, unlike enthalpy, can be found explicitly. Entropy specifically is a measure of the number of microstates available to a chemical system. Microstates are individual possible states of the system, where a state is a particular arrangement of positions for particles and a particular distribution of kinetic energy among those particles. This can be calculated as shown in Equation 5.6, where S is the entropy, k is Boltzmann’s constant, and W is the number of available microstates. S=klnW
Thermodynamics
Published in Harshad K. D. H. Bhadeshia, Theory of Transformations in Steels, 2021
The Boltzmann relation S=kln{wc} links the entropy to the logarithm of the number of microstates wc that a given macroscopic state of the system can have. The change in entropy in going from a completely ordered spin state to one which is completely disordered is given therefore by Nakln{2sa+1}
History of ‘temperature’: maturation of a measurement concept
Published in Annals of Science, 2020
But in 1877, Boltzmann used probability to explore the fact that the speeds and thus the momenta of molecules vary.142 He determined that the probability that some combination of positions and velocities would produce a macroscopic property such as temperature was equal to a number raised to the power of the entropy. Also, since probability here could be calculated by simply counting the number of ways the macroscopic property could be produced, entropy is equal to the logarithm of the number of microstates that produce some macrostate. Boltzmann did not formulate this discovery as we do now, S = k ln W, or use the discovery to much change his thinking about temperature. He did not, for example, use it in any substantial way in his Lectures on Gas Theory, published twenty years later. His colleagues, too, gave it little attention. Max Planck, for example, did not use it in his Treatise on Thermodynamics in 1897.
Entropy minimization study of Maxwell nanofluid flow using oxides nanoparticles under transpiration and magnetic dissipation effects
Published in Numerical Heat Transfer, Part A: Applications, 2023
Shahzad Munir, Muhammad Ahmed, Ammara Amin
The entropy parameter increases as the nanomaterial volume fraction is increased, as shown in Figure 4c. This entropy behavior is due to increment in heat transfer for higher volume fraction Furthermore, width of thermal boundary layer is smaller for base fluid and larger for This is due to the higher thermal conductivity of nanofluid and lower thermal conductivity of water. Figure 4d shows the effect of on It is recorded that higher transverse magnetic parameter substantially assist to higher entropy values of any under discussion system. Consequently, by reducing the magnetic flux, we can attain the key purpose of the second law of thermodynamics, which is entropy minimization. From Figure 4e, which describes the impact of on it is recorded that attain higher values for large This is because, temperature difference drives the flow of heat from the hotter region to the colder region. The increased temperature gradient promotes energy transfer and randomizes the distribution of energy among the particles. This increased randomness increases the number of microstates available to the system and, consequently, an increase in entropy.