Lectures in Classical Thermodynamics with an Introduction to Statistical Mechanics

2020 ◽  
Author(s):  
Daniel Blankschtein
Keyword(s):  
Statistical Mechanics ◽  
Classical Thermodynamics

Entropy: Part I — Statistics and its Misleading Disorder

1999 ◽  
Author(s):  
Elias P. Gyftopoulos
Keyword(s):  
Statistical Mechanics ◽  
Equilibrium State ◽  
Experimental Evidence ◽  
Statistical Interpretation ◽  
Statistical Entropy ◽  
Thermodynamic Entropy ◽  
Perfect Order ◽  
Natural Tendency ◽  
Classical Thermodynamics ◽  
Thermodynamic Equilibrium State

Abstract The overwhelming majority of scientists, engineers, and other professionals believe that: (a) statistical mechanics explains thermodynamics, and provides explicit expressions of entropy (for example, S = k ln Ω); and (b) in general, each entropy represents disorder in a system and, in particular for given values of energy, volume, and amounts of constituents, the largest value of the entropy represents the ultimate disorder (thermodynamic equilibrium state). The purposes of this paper are to present both theoretical and experimental evidence that refutes these beliefs and to show that the spontaneous increase in thermodynamic entropy represents a nonstatistical, natural tendency to perfect order rather than disorder. The arguments are presented in two parts. Brief discussions of the premises and conclusions of the statistical interpretation of thermodynamics, the association of the statistical entropy with disorder, and inconsistencies that arise from such an association are presented in Part I. A nonstatistical exposition of thermodynamics, the interpretation of entropy as a measure of the quantum-theoretic shape of molecules, and the association of the entropy of classical thermodynamics with perfect order are presented in Part II.

scholarly journals SEVERE CHALLENGES IN GRAVITY THEORIES

2012 ◽  
Vol 07 ◽  
pp. 219-226
Author(s):  
YUAN K. HA
Keyword(s):  
Statistical Mechanics ◽  
Attractive Force ◽  
Fundamental Interaction ◽  
Quantum Theories ◽  
Fundamental Interactions ◽  
Underlying Theory ◽  
Theories Of Gravity ◽  
Gravity Theories ◽  
Classical Thermodynamics

Gravity is specifically the attractive force between two masses separated at a distance. Is this force a derived or a fundamental interaction? We believe that all fundamental interactions are quantum in nature but a derived interaction may be classical. Severe challenges have appeared in many quantum theories of gravity. None of these theories has thus far attained its goal in quantizing gravity and some have met remarkable defeat. We are led to ponder whether gravitation is intrinsically classical and that there would exist a deeper and structurally different underlying theory which would give rise to classical gravitation, in the sense that statistical mechanics, quantum or classical, provides the underlying theory of classical thermodynamics.

Statistical Interpretation of Entropy

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Statistical Mechanics ◽  
Thermodynamic Model ◽  
Point Of View ◽  
Statistical Interpretation ◽  
Conservation Of Energy ◽  
Heat Engines ◽  
Lower Temperature ◽  
Intuitive Grasp ◽  
The Individual ◽  
Classical Thermodynamics

As we have seen, thermodynamics is based for the most part on the idea of the conservation of energy (First Law) and the concept of entropy (Second Law). The conservation of energy gives little problem intuitively, but it is quite another story with entropy. Entropy can be considered from the point of view of idealized heat engines operating in cycles, or by deriving some of its inherent properties (Chapter 5). We will see how it is measured and tabulated in Chapter 7. This is all very useful, but doesn't help much in gaining an intuitive grasp of entropy, such as we have for the other thermodynamic parameters. Just what is entropy, anyway? There may not be any definitive short answer to this question. If we had to rely on classical thermodynamics for an answer, we would talk at some length about the availability of energy, e.g., the fact that in spite of the tremendous quantity of energy in the ocean, we cannot use any of it to power a ship or to do anything else; the ocean's thermal energy is unavailable unless we provide a reservoir for heat at a lower temperature. This is of course perfectly true, and many useful discussions of the meaning of entropy follow this line of thought, but somehow after all these discussions, the entropy remains somewhat elusive. There is, however, another way to think of entropy that is by far the most useful, and that is from the statistical/probability point of view. This requires that we consider matter from the point of view of the individual particles (atoms, molecules, ions) rather than as macroscopic, homogeneous bodies, and is therefore not a part of classical thermodynamics, but of statistical mechanics. In this chapter we present the rudiments of this approach, not so that the reader can become proficient in statistical thermodynamics (a considerably more thorough introduction is required for that) but to show how entropy is related to statistical considerations. Statistical mechanics does not exactly explain what entropy is, but rather provides a model, quite different from the thermodynamic model, that contains a parameter identical to the entropy of the thermodynamic model in every measurable respect.

A non-extensive statistical physics view in Earth Physics: Geodynamic properties in terms of Complexity theory .

2020 ◽  
Author(s):  
Filippos Vallianatos
Keyword(s):  
Statistical Mechanics ◽  
Gaussian Distribution ◽  
Plate Tectonics ◽  
Statistical Physics ◽  
Extreme Values ◽  
Global Scale ◽  
Coda Wave ◽  
Research And Innovation ◽  
Classical Thermodynamics ◽  
Earth Dynamics

<p>Boltzmann-Gibbs (BG) statistical physics is one of the cornerstones of contemporary physics. It establishes a remarkably useful bridge between the mechanical microscopic laws and macroscopic description using classical thermodynamics. If long-range interactions, non-markovian microscopic memory, multifractal boundary conditions and multifractal structures are present then another type of statistical mechanics, than BG, seems appropriate to describe nature (Tsallis, 2001).</p><p>To overcome at least some of these anomalies that seem to violate BG statistical mechanics, non-extensive statistical physics (NESP) was proposed by Tsallis  (Tsallis, 1988) that recovers the extensive BG as a particular case. The associated generalized entropic form controlled by the entropic index  q that represents a measure of non-additivity of a system. S<sub>q</sub> recovers S<sub>BG</sub> in the limit q→1. For a variable X with a probability distribution p(X), as that of seismic moment , inter-event times  or distances between the successive earthquakes or the length of faults in a given region, using terms of NESP, we obtain the physical probability which expressed by a q-exponential function as defined in Tsallis, (2009).  Another type of distributions that are deeply connected to statistical physics is that of the squared variable X<sup>2</sup>. In BG statistical physics, the distribution of X<sup>2</sup> corresponds to the well-known Gaussian distribution. If we optimize S<sub>q</sub> for X<sup>2</sup>, we obtain a generalization of the normal Gaussian that is known as q-Gaussian distribution (Tsallis, 2009). In the limit q→1, the normal Gaussian distribution, recovered. For q> 1, the q-Gaussian distribution has power-law tails with slope -2/(q-1), thus enhancing the probability of the extreme values.</p><p>In the present work we review a collection of Earth physics problems such as a) NESP pathways in earthquake size distribution, b) The effect of mega-earthquakes, c) Spatiotemporal description of Seismicity, d) the plate tectonics as a case of non-extensive thermodynamics e) laboratory seismology and fracture, f) the non-extensive nature of earth’s ambient noise, and g) evidence of non-extensivity in eartquakes’ coda wave. The aforementioned cases cover the most of the problems in Earth Physics indicated that non extensive statistical physics could be the underline interpretation tool to understand earth's evolution and dynamics.</p><p>We can state that the study of the non-extensive statistical physics of earth dynamics remains wide-open with many significant discoveries to be made. The results of the analysis in the cases described previously indicate that the ideas of NESP can be used to express the non-linear dynamics that control the evolution of the earth dynamics at different scales. The key scientific challenge is to understand in a unified way, using NESP principles, the physical mechanisms that drive the evolution of fractures ensembles in laboratory and global scale and how we can use measures of evolution that will forecast the extreme fracture event rigorously and with consistency.</p><p><strong> </strong><strong>Acknowledgments. </strong>We acknowledge support by the project “HELPOS – Hellenic System for Lithosphere Monitoring” (MIS 5002697) which is implemented under the Action “Reinforcement of the Research and Innovation Infrastructure”, funded by the Operational Programme "Competitiveness, Entrepreneurship and Innovation" (NSRF 2014-2020) and co-financed by Greece & European Union (ERDF).</p><p><strong> </strong></p>

Demystifying Thermodynamics by Connecting It With Mechanics

2008 ◽  
Author(s):  
W. John Dartnall ◽  
John Reizes ◽  
Geoff Anstis
Keyword(s):  
Statistical Mechanics ◽  
Newtonian Mechanics ◽  
Empirical Relationships ◽  
Classical View ◽  
Classical Structure ◽  
Laws Of Thermodynamics ◽  
Mechanical Models ◽  
The Many ◽  
Classical Thermodynamics

The laws of thermodynamics provide an adequate basis for the development of classical thermodynamics and for the many empirical relationships used by mechanical and chemical engineers. The laws evolved before the advent of the computer with its ability to handle complex simulations. This led to the classical structure that did not require a molecular view of matter. The concept of entropy grew out of this classical view but, has unfortunately earned a reputation for being something mysterious and difficult. Statistical mechanics, much of which is based on Newtonian mechanics, has the power to remove the mystery. But, because of its mathematical complexity, it has rarely been used by engineers either to clarify understanding or to analyze processes and models. We propose, illustrating with examples, that simple Newtonian mechanical models can be used in place of statistical mechanics — at least for the teaching of concepts. Surprisingly, the models developed using Newton’s three Laws allow the development of the zeroth, first and second laws of thermodynamics and the processes by which equilibrium is reached. We believe that in teaching thermodynamics the links with Newtonian mechanics would best be established by the proposed simple methods because of the resulting enlivening of Newtonian mechanics and the enhanced understanding of the fundamental concepts of thermodynamics.

Should Engineering Thermodynamics Include a Simplified Treatment of Its Underlying Molecular Basis?

2009 ◽  
Author(s):  
W. John Dartnall ◽  
John Reizes ◽  
Geoff Anstis
Keyword(s):  
Statistical Mechanics ◽  
Molecular Basis ◽  
Hard Spheres ◽  
Mechanistic Explanation ◽  
Carnot Cycle ◽  
Undergraduate Level ◽  
State Laws ◽  
One Dimensional ◽  
Laws Of Thermodynamics ◽  
Classical Thermodynamics

Engineering Thermodynamics is commonly treated at undergraduate level as “classical thermodynamics and its applications”. Recent publications, using one dimensional simulations employing hard spheres have proposed ways to obtain the laws of thermodynamics. These models help to explain the state laws, the limitation of the Carnot cycle relationship as well as difficult concepts like entropy. The models, although deterministic, are able to demonstrate the probabilistic behaviour, normally explained by the mathematically sophisticated derivations of Statistical Mechanics. Is it time to include a simplified, mechanistic explanation of Engineering Thermodynamics by deriving it from its molecular basis?

On a Scale-Invariant Model of Statistical Mechanics and the Laws of Thermodynamics

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Statistical Mechanics ◽  
Thermal Energy ◽  
Thermodynamic System ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Scale Invariant ◽  
Invariant Model ◽  
Definition Of ◽  
Classical Thermodynamics ◽  
Total Thermal Energy

A scale-invariant model of statistical mechanics is applied to describe modified forms of zeroth, first, second, and third laws of classical thermodynamics. Following Helmholtz, the total thermal energy of the thermodynamic system is decomposed into free heat U and latent heat pV suggesting the modified form of the first law of thermodynamics Q = H = U + pV. Following Boltzmann, entropy of ideal gas is expressed in terms of the number of Heisenberg–Kramers virtual oscillators as S = 4 Nk. Through introduction of stochastic definition of Planck and Boltzmann constants, Kelvin absolute temperature scale T (degree K) is identified as a length scale T (m) that is related to de Broglie wavelength of particle thermal oscillations. It is argued that rather than relating to the surface area of its horizon suggested by Bekenstein (1973, “Black Holes and Entropy,” Phys. Rev. D, 7(8), pp. 2333–2346), entropy of black hole should be related to its total thermal energy, namely, its enthalpy leading to S = 4Nk in exact agreement with the prediction of Major and Setter (2001, “Gravitational Statistical Mechanics: A Model,” Classical Quantum Gravity, 18, pp. 5125–5142).

scholarly journals Statistical Mechanics at Strong Coupling: A Bridge between Landsberg’s Energy Levels and Hill’s Nanothermodynamics

Nanomaterials ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2471
Author(s):  
Rodrigo de Miguel ◽  
J. Miguel Rubí
Keyword(s):  
Statistical Mechanics ◽  
Strong Coupling ◽  
Energy Landscape ◽  
Energy Levels ◽  
Heat Bath ◽  
Temperature Dependent ◽  
Thermodynamic Variable ◽  
The 1950S ◽  
Classical Thermodynamics

We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill’s nanothermodynamics.

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