The Nernst Postulate: The Third Law of Thermodynamics

2019 ◽  
pp. 223-228
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Specific Heat ◽  
Quantum Statistical Mechanics ◽  
Thermodynamic System ◽  
Zero Temperature ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Quantum Statistical

The Nernst postulate, or Third Law of Thermodynamics, is derived from quantum statistical mechanics. It states, ‘The entropy of a thermodynamic system goes to a constant as the temperature goes to zero.’ The main consequences are that specific heat and compressibility goes to zero as temperature goes to zero. Both are demonstrated. It is shown that, both with and without the Nernst postulate, zero temperature is not experimentally attainable. Gases are usually well behaved in this respect, but we all know from experience that molecules of H2O can clump together, form drops, and rain on us.

Quantum Canonical Ensemble

2019 ◽  
pp. 297-321
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Quantum Statistical Mechanics ◽  
Harmonic Oscillators ◽  
Quantum Mechanical ◽  
The Third ◽  
Two Level Systems ◽  
Third Law ◽  
Quantum Statistical ◽  
The Relationship

This chapter introduces the quantum mechanical canonical ensemble, which is used for the majority of problems in quantum statistical mechanics. The ensemble is derived and analogies with the classical ensemble are presented. A useful expression for the quantum entropy is derived. The origin of the Third Law is explained. The relationship between fluctuations and derivatives found in classical statistical mechanics is shown to have counterparts in quantum statistical mechanics. The factorization of the partition function is re-introduced as the best trick in quantum statistical mechanics. Due to their importance in later chapters, basic calculations of the properties of two-level systems and simple harmonic oscillators are derived.

THE THIRD LAW OF THERMODYNAMICS

1987 ◽  
Vol 01 (01n02) ◽  
pp. 61-66 ◽  
Author(s):  
JACEK MIĘKISZ ◽  
CHARLES RADIN
Keyword(s):  
General Class ◽  
Finite Range ◽  
Zero Temperature ◽  
One Dimensional ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
Third Law

We consider a very general class of discrete classical one dimensional statistical mechanical models and prove that generic finite range interactions have crystalline zero temperature ensembles, and in particular satisfy the third law of thermodynamics.

scholarly journals BLACK HOLES AND THE THIRD LAW OF THERMODYNAMICS

2004 ◽  
Vol 13 (04) ◽  
pp. 739-770 ◽  
Author(s):  
F. BELGIORNO ◽  
M. MARTELLINI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Second Law Of Thermodynamics ◽  
Temperature Limit ◽  
Black Hole Thermodynamics ◽  
Zero Temperature ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Extremal Black Holes

We discuss in the framework of black hole thermodynamics some aspects relative to the third law in the case of black holes of the Kerr–Newman family. In the light of the standard proof of the equivalence between the unattainability of the zero temperature and the entropic version of the third law it is remarked that the unattainability has a special character in black hole thermodynamics. Also the zero temperature limit which obtained in the case of very massive black holes is discussed and it is shown that a violation of the entropic version in the charged case occurs. The violation of the Bekenstein–Hawking law in favour of zero entropy SE=0 in the case of extremal black holes is suggested as a natural solution for a possible violation of the second law of thermodynamics. Thermostatic arguments in support of the unattainability are explored, and SE=0 for extremal black holes is shown to be again a viable solution. The third law of black hole dynamics by W. Israel is then interpreted as a further strong corroboration to the picture of a discontinuity between extremal states and non-extremal ones.

scholarly journals Some Implications of a Scale Invariant Model of Statistical Mechanics to Boltzmann versus Shannon Entropy in Thermodynamics and Information Theory

2021 ◽  
Vol 20 ◽  
pp. 56-65
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Comparative Study ◽  
Shannon Entropy ◽  
Scale Invariant ◽  
Invariant Model ◽  
Shannon's Entropy ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Third Law

A scale invariant model of statistical mechanics is applied for a comparative study of Boltzmann’s entropy in thermodynamics versus Shannon’s entropy in information theory. The implications of the model to the objective versus subjective aspects of entropy as well as Nernst-Planck statement of the third law of thermodynamics are also discussed

scholarly journals DEFORMED SPECIAL RELATIVITY WITH AN ENERGY BARRIER OF A MINIMUM SPEED

2010 ◽  
Vol 19 (05) ◽  
pp. 539-564 ◽  
Author(s):  
CLÁUDIO NASSIF
Keyword(s):  
Energy Barrier ◽  
Flat Space ◽  
Background Field ◽  
Inertial Reference Frame ◽  
Zero Temperature ◽  
Relativistic Dynamics ◽  
The Third ◽  
Minimum Speed ◽  
Third Law Of Thermodynamics ◽  
Third Law

This paper aims to introduce a new principle of symmetry in the flat space–time by means of the elimination of the classical idea of rest, and by including a universal minimum limit of speed in the quantum world. Such a limit, unattainable by the particles, represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. So there emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting implications of the existence of such a minimum speed is that it prevents the absolute zero temperature for an ultracold gas, according to the third law of thermodynamics. So we will be able to provide a fundamental dynamical explanation for the third law by means of a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed.

The third law of thermodynamics for Kerr black holes

1991 ◽  
Vol 250 (2) ◽  
pp. 300-309 ◽  
Author(s):  
Isao Okamoto ◽  
Osamu Kaburaki
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Rate Of Change ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
The Third ◽  
Proportionality Constant ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Kerr Black Holes

Abstract At first the thermodynamic and evolutionary properties of Kerr black holes are clarified using the M–J plane, where M is the hole’s mass and J is its angular momentum. In this plane Schwarzschild black holes with h = 0 are distributed along the M-axis and extreme Kerr holes with h = 1 lie on the line J = M2, where $h \equiv J/4S$ is a non-dimensional parameter and S is the entropy. Taking into account possible accretion processes, we then derive the condition under which the third law of black-hole thermodynamics for Kerr holes is not violated. The condition is given in the form of as $\alpha \ge 1$, where the rate of change of a hole’s state, dh/dM, is proportional to $(1-h)^\alpha$ in the neighbourhood of $h \simeq 1$. If the rate is proportional to the vanishing surface gravity, gH, with which the hole has to accrete matter and angular momentum, α is given by $\alpha= 1+2/C$, where $dh/dM=Cg_\text H=C(1-h^2)/4M$, and C is a proportionality constant. In this case M, J and S diverge to infinity as a power law for $h \to 1$, and therefore no Kerr holes can reach the extreme Kerr state with the absolute zero temperature by accreting finite amounts of mass and angular momentum.

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