Boltzmann Entropy & Equilibrium in Non-Isolated Systems

2017 ◽  
pp. 74-92 ◽  
Author(s):  
Alberto Gianinetti
Keyword(s):  
Statistical Mechanics ◽  
Stable Condition ◽  
Microscopic Level ◽  
Boltzmann Entropy ◽  
Microscopic Approach ◽  
Macroscopic Level ◽  
Probable Distribution ◽  
Isolated Systems ◽  
Most Probable Distribution

The microscopic approach of statistical mechanics has developed a series of formal expressions that, depending on the different features of the system and/or process involved, allow for calculating the value of entropy from the microscopic state of the system. This value is maximal when the particles attain the most probable distribution through space and the most equilibrated sharing of energy between them. At the macroscopic level, this means that the system is at equilibrium, a stable condition wherein no net statistical force emerges from the overall behaviour of the particles. If no force is available then no work can be done and the system is inert. This provides the bridge between the probabilistic equilibration that occurs at the microscopic level and the classical observation that, at a macroscopic level, a system is at equilibrium when no work can be done by it.

Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 846-850 ◽  
Author(s):  
M. Leung ◽  
C. K. Hsieh ◽  
D. Y. Goswami
Keyword(s):  
Surface Roughness ◽  
Statistical Mechanics ◽  
Theoretical Basis ◽  
Rough Surfaces ◽  
Electrical Contact ◽  
Height Distribution ◽  
Probable Distribution ◽  
Theoretical Predictions ◽  
Most Probable Distribution ◽  
Roughness Measurements

In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Boltzmann: the probabilistic interpretation of entropy

2020 ◽  
pp. 570-595
Author(s):  
Robert T. Hanlon
Keyword(s):  
Probability Theory ◽  
Statistical Mechanics ◽  
Gas Phase ◽  
Probabilistic Interpretation ◽  
Atoms And Molecules ◽  
Collective Work ◽  
Novel Approach ◽  
Probable State ◽  
Probable Distribution ◽  
Most Probable Distribution

Boltzmann’s collective work was a mathemetical tour de force. Building on Clausius and Maxwell, he demonstrated that the distribution of gas phase atoms and molecules follows from probability theory. Atoms and molecules distribute themselves in space and momentum to the most probable distribution. Boltzmann used probability theory to quantify the most probable state and then demonstrated the connection between this state and its entropy. This novel approach, later validated by Sackur–Tetrode, led to the creation of statistical mechanics.

Statistical Thermodynamics Concepts and Mathematical Tools for a Multi-Agent Ecosystem

2014 ◽  
Vol 20 (2) ◽  
pp. 237-270
Author(s):  
Javier Segovia
Keyword(s):  
Statistical Mechanics ◽  
Mathematical Problem ◽  
Statistical Thermodynamics ◽  
Economic Systems ◽  
Global Behavior ◽  
Probable Distribution ◽  
Or Economics ◽  
Artificial Ecosystems ◽  
Multi Agent ◽  
Most Probable Distribution

Finding the distribution of systems over their possible states is a mathematical problem. One possible solution is the method of the most probable distribution developed by Boltzmann. This method has been instrumental in developing statistical mechanics and explaining the origin of many thermodynamics concepts, like entropy or temperature, but is also applicable in many other fields like ecology or economics. Artificial ecosystems have many features in common with ecological or economic systems, but surprisingly the method does not appear to have been very successful in this field of application. The hypothesis of this article is that this failure is due to the incorrect interpretation of the method's concepts and mathematical tools. We propose to review and reinterpret the method so that it can be correctly applied and all its potential exploited in order to study and characterize the global behavior of an artificial multi-agent ecosystem.

From Nature’s Tendency To Statistical Mechanics

2017 ◽  
pp. 56-60
Author(s):  
Alberto Gianinetti
Keyword(s):  
Statistical Mechanics ◽  
Macroscopic Level

Some processes happen spontaneously. What, at a macroscopic level, appears as a nature’s tendency, is an effect of the complex statistical behaviour of the microscopic particles: their overall net effect emerges at the macroscopic level as a spontaneous force that determines if and how a system can spontaneously change, and if and toward which direction a process is therefore started.

Hypokinetic Movement Disorders: Parkinson Disease

2021 ◽  
pp. 576-582
Author(s):  
Sarah M. Tisel ◽  
Bryan T. Klassen
Keyword(s):  
Cell Death ◽  
Substantia Nigra ◽  
Parkinson Disease ◽  
Movement Disorder ◽  
Movement Disorders ◽  
Dopaminergic Neurons ◽  
Microscopic Level ◽  
Rest Tremor ◽  
Macroscopic Level ◽  
Progressive Degeneration

Parkinson disease (PD) is the classic hypokinetic movement disorder and one of the most common and widely recognized neurodegenerative conditions. PD is distinct from parkinsonism, a term that refers to a syndrome of rest tremor, bradykinesia, rigidity, and postural instability. The mechanism behind the progressive degeneration and cell death that result in PD is not precisely understood. Substantia nigra depigmentation occurs on a macroscopic level and loss of dopaminergic neurons and gliosis on a microscopic level.

Dual-Level Attack Detection, Characterization and Response for Networks Under DDoS Attacks

2011 ◽  
Vol 3 (1) ◽  
pp. 1-20
Author(s):  
Anjali Sardana ◽  
Ramesh C. Joshi
Keyword(s):  
Network Performance ◽  
Attack Detection ◽  
Microscopic Level ◽  
Collateral Damage ◽  
Ddos Attacks ◽  
Response Mechanism ◽  
Macroscopic Level ◽  
Coarse Level ◽  
Network Functionality ◽  
In Transit

DDoS attacks aim to deny legitimate users of the services. In this paper, the authors introduce dual - level attack detection (D-LAD) scheme for defending against the DDoS attacks. At higher and coarse level, the macroscopic level detectors (MaLAD) attempt to detect congestion inducing attacks which cause apparent slowdown in network functionality. At lower and fine level, the microscopic level detectors (MiLAD) detect sophisticated attacks that cause network performance to degrade gracefully and stealth attacks that remain undetected in transit domain and do not impact the victim. The response mechanism then redirects the suspicious traffic of anomalous flows to honeypot trap for further evaluation. It selectively drops the attack packets and minimizes collateral damage in addressing the DDoS problem. Results demonstrate that this scheme is very effective and provides the quite demanded solution to the DDoS problem.

Method of most probable distribution: New solutions and results

Pramana ◽  
1989 ◽  
Vol 33 (4) ◽  
pp. 455-465 ◽  
Author(s):  
V J Menon ◽  
D C Agrawal
Keyword(s):  
Probable Distribution ◽  
Most Probable Distribution

scholarly journals NONLINEAR EXTENSIONS OF SCHRÖDINGER–VON NEUMANN QUANTUM DYNAMICS: A SET OF NECESSARY CONDITIONS FOR COMPATIBILITY WITH THERMODYNAMICS

2005 ◽  
Vol 20 (13) ◽  
pp. 977-984 ◽  
Author(s):  
GIAN PAOLO BERETTA
Keyword(s):  
Quantum Dynamics ◽  
Necessary Conditions ◽  
Experimental Tests ◽  
Microscopic Level ◽  
General Description ◽  
Von Neumann ◽  
Nonequilibrium States ◽  
Nonlinear Extensions ◽  
Isolated Systems ◽  
True Quantum

We propose a list of conditions that consistency with thermodynamics imposes on linear and nonlinear generalizations of standard unitary quantum mechanics that assume a set of true quantum states without the restriction ρ2 = ρ even for strictly isolated systems and that are to be considered in experimental tests of the existence of intrinsic (spontaneous) decoherence at the microscopic level. As part of the discussion, we present a general description of nonequilibrium states.

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