scholarly journals The Second Law Of Thermodynamics as a Force Law

2018 ◽  
Author(s):  
Jürgen Schlitter
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Chemical Reactions ◽  
Driving Force ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Constant Energy ◽  
Wide Range

The second law of thermodynamics states the increase of entropy, ΔS > 0, for real processes from state A to state B at constant energy from chemistry over biological life and engines to cosmic events. The connection of entropy to information, phase-space and heat is helpful, but does not immediately convince observers of the validity and basis of the second law. This gave grounds for finding a rigorous, but more easily acceptable reformulation. Here we show using statistical mechanics that this principle is equivalent to a force law ⟨⟨f⟩⟩> 0 in systems where mass centres and forces can be identified. The sign of this net force - the average mean force along a path from A to B - determines the direction of the process. The force law applies to a wide range of processes from machines to chemical reactions. The explanation of irreversibility by a driving force appears more plausible than the traditional formulation as it emphasizes the cause instead of the effect of motions.

scholarly journals The Second Law Of Thermodynamics as a Force Law

2018 ◽  
Author(s):  
Jürgen Schlitter
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Chemical Reactions ◽  
Driving Force ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Constant Energy ◽  
Wide Range

The second law of thermodynamics states the increase of entropy, Delta S > 0, for real processes from state A to state B at constant energy from chemistry over biological life and engines to cosmic events. The connection of entropy to information, phase-space and heat is helpful, but does not immediately convince observers of the validity and basis of the second law. This gave grounds for finding a rigorous, but more easily acceptable reformulation. Here we show using statistical mechanics that this principle is equivalent to a force law ⟨⟨f⟩⟩> 0 in systems where mass centres and forces can be identified. The sign of this net force - the average mean force along a path from A to B - determines the direction of the process. The force law applies to a wide range of processes from machines to chemical reactions. The explanation of irreversibility by a driving force appears more plausible than the traditional formulation as it emphasizes the cause instead of the effect of motions.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

Supradegeneracy and the Second Law of Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 121-132
Author(s):  
Daniel P. Sheehan
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Population Inversion ◽  
Laboratory Experiments ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Boltzmann Factor ◽  
Energy Currents ◽  
Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

scholarly journals A GENERAL INFORMATION THEORETICAL PROOF FOR THE SECOND LAW OF THERMODYNAMICS

2008 ◽  
Vol 17 (03) ◽  
pp. 531-537 ◽  
Author(s):  
QI-REN ZHANG
Keyword(s):  
Statistical Mechanics ◽  
Quantum State ◽  
Second Law Of Thermodynamics ◽  
General Information ◽  
Second Law ◽  
Classical Physics ◽  
Interaction Information ◽  
Entropy Increase ◽  
Classical Statistical Mechanics ◽  
Social Statistics

We show that the conservation and the non-additivity of information, together with the additivity of entropy makes entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true, not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive.

scholarly journals A Pedagogical Approach to Obtain the Combined First and Second Law of Thermodynamics from Classical Statistical Mechanics

2021 ◽  
Author(s):  
Ananth Govind Rajan
Keyword(s):  
Kinetic Energy ◽  
Statistical Mechanics ◽  
General System ◽  
Second Law Of Thermodynamics ◽  
Average Kinetic Energy ◽  
Second Law ◽  
Pedagogical Approach ◽  
Classical Statistical Mechanics ◽  
System Pressure ◽  
Many Body Interactions

The combined first and second law of thermodynamics for a closed system is written as dE=TdS - PdV, where E is the internal energy, S is the entropy, V is the volume, T is the temperature, and P is the pressure of the system. This equation forms the basis for understanding physical phenomena ranging from heat engines to chemical reactors to biological systems. In this work, we present a pedagogical approach to obtain the combined first and second law of thermodynamics beginning with the principles of classical statistical mechanics, thereby establishing a fundamental link between energy conservation, heat, work, and entropy. We start with Boltzmann's entropy formula and use differential calculus to establish this link. Some new aspects of this work include the use of the microcanonical ensemble, which is typically considered to be intractable, to write the partition function for a general system of matter; deriving the average of the inverse kinetic energy, which appears in the microcanonical formulation of the combined first and second law, and showing that it is equal to the inverse of the average kinetic energy; obtaining an expression for the pressure of a system involving many-body interactions; and introducing the system pressure in the combined first and second law via Clausius's virial theorem. Overall, this work informs the derivation of fundamental thermodynamic relations from an understanding of classical statistical mechanics. The material presented herein could be incorporated into senior undergraduate/graduate-level courses in statistical thermodynamics and/or molecular simulations.

4. The arrow of time

2021 ◽  
pp. 64-79
Author(s):  
Jenann Ismael
Keyword(s):  
Statistical Mechanics ◽  
Laws Of Nature ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Arrow Of Time ◽  
Temporal Asymmetry ◽  
The Everyday ◽  
Everyday World ◽  
Laws Of Motion

‘The arrow of time’ discusses where the arrow of time comes from. The fundamental laws of motion do not distinguish past and future. And yet the everyday world is full of manifestly asymmetric processes. This chapter discusses the apparent mismatch between the fundamental laws of nature and the manifest asymmetry of the everyday world. The temporal asymmetry is made precise by the second law of thermodynamics and the tension between the second law and the fundamental laws is addressed by the development of statistical mechanics.

scholarly journals Testing the weak cosmic censorship conjecture in torus-like black hole under charged scalar field

2020 ◽  
Vol 29 (12) ◽  
pp. 2050078
Author(s):  
Wei Hong ◽  
Benrong Mu ◽  
Jun Tao
Keyword(s):  
Black Hole ◽  
Phase Space ◽  
Scalar Field ◽  
Second Law Of Thermodynamics ◽  
Cosmic Censorship ◽  
Second Law ◽  
Complex Scalar ◽  
Charged Scalar ◽  
First Law Of Thermodynamics ◽  
Cosmic Censorship Conjecture

We investigate weak cosmic censorship conjecture in charged torus-like black hole by the complex scalar field scattering. Using the relation between the conserved quantities of a black hole and the scalar field, we can calculate the change of the energy and charge within the infinitesimal time. The change of the enthalpy is connected to the change of energy, then we use those results to test whether the first law, the second law as well as the weak cosmic censorship conjecture are valid. In the normal phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid, and the second law of thermodynamics is not violated. For the specific black hole under scalar field scattering we consider, in the extended phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid. However, the second law of thermodynamics is violated when the black hole’s initial charge reaches a certain value.

scholarly journals TRANSITION AND EVOLUTION OF INFORMATION AT THE MICROSCOPIC LEVEL

T-Comm ◽  
2021 ◽  
Vol 15 (5) ◽  
pp. 62-66
Author(s):  
Aleksey V. Yudenkov ◽  
◽  
Aleksandr M. Volodchenkov ◽  
Liliya P. Rimskaya ◽  
◽  
...  
Keyword(s):  
Information Theory ◽  
Phase Space ◽  
Information Technologies ◽  
Second Law Of Thermodynamics ◽  
Mathematic Model ◽  
Second Law ◽  
Space Model ◽  
Discrete Phase ◽  
Markovian Systems ◽  
Phase Space Model

A simultaneous development of the fundamental research areas of the information theory is needed for efficient development in the information technologies. It is known that for the complicated macroscopic systems information evolution may be shaped on the basis of the principal thermodynamics laws (the second law of thermodynamics, etc). At the same time it is not known whether the fundamentals of the information theory for the macroscopic systems may be applicable to the microscopic systems. The study works out a mathematic model of the discrete phase space adapted to describing the evolution of information (entropy) of the microscopic systems. The discrete phase-space model rests on the indeterminacy principle and fundamental properties of the discrete continuous-time Markovian systems. The Kolmogorov equations represent the main mathematical tools technique. The suggested model refers to the smallest metric scale when the external macroscopic observation is possible. This scale can be viewed as a quasiclassical level. The research results are the following. The structure of the phase space of the elementary signal is revealed. It is demonstrated that the entropy of the microscopic systems increases, i.e. for the microscopic systems the second law of thermodynamics is true. There has been demonstrated transition from the microscopic model to the macroscopic one thus proving the former’s adequacy. The discrete phase-space model is promising in the aspect of further development. For example, it can be applied to the physical systems “particle – field”. The approach represented by the model will allow to study electromagnetic and gravity fields at the quasiclassical level. The above model of the discrete phase space and its application in the study of the evolution of the microscopic systems is a proprietary design of the authors.

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