Statistical Mechanics of Interacting Systems: Theory of Phase Transitions

2005 ◽  
pp. 253-255 ◽  
Keyword(s):  
Phase Transitions ◽  
Statistical Mechanics ◽  
Systems Theory ◽  
Interacting Systems

Introduction

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Phase Transitions ◽  
Statistical Mechanics ◽  
Conservation Laws ◽  
Law Of Large Numbers ◽  
Macroscopic Scale ◽  
Classical Probability ◽  
Large Numbers ◽  
Microscopic World ◽  
New Phenomena

Statistical mechanics concerns the transition from the microscopic to the macroscopic realm. On a macroscopic scale new phenomena arise that have no counterpart in the microscopic world. For example, macroscopic systems have a temperature; they might undergo phase transitions; and their dynamics may involve dissipation. How can such phenomena be explained? This chapter discusses the characteristic differences between the microscopic and macroscopic realms and lays out the basic challenge of statistical mechanics. It suggests how, in principle, this challenge can be tackled with the help of conservation laws and statistics. The chapter reviews some basic notions of classical probability theory. In particular, it discusses the law of large numbers and illustrates how, despite the indeterminacy of individual events, statistics can make highly accurate predictions about totals and averages.

Chapter 22. Connections to Statistical Physics

2021 ◽  
Author(s):  
Fabrizio Altarelli ◽  
Rémi Monasson ◽  
Guilhem Semerjian ◽  
Francesco Zamponi
Keyword(s):  
Phase Transitions ◽  
Low Temperature ◽  
Statistical Mechanics ◽  
Cost Function ◽  
Computer Science ◽  
Statistical Physics ◽  
Energy Landscape ◽  
Research Activity ◽  
Detailed Picture ◽  
Intense Research

This chapter surveys a part of the intense research activity that has been devoted by theoretical physicists to the study of randomly generated k-SAT instances. It can be at first sight surprising that there is a connection between physics and computer science. However low-temperature statistical mechanics concerns precisely the behaviour of the low-lying configurations of an energy landscape, in other words the optimization of a cost function. Moreover the ensemble of random k-SAT instances exhibit phase transitions, a phenomenon mostly studied in physics (think for instance at the transition between liquid and gaseous water). Besides the introduction of general concepts of statistical mechanics and their translations in computer science language, the chapter presents results on the location of the satisfiability transition, the detailed picture of the satisfiable regime and the various phase transitions it undergoes, and algorithmic issues for random k-SAT instances.

The statistical mechanics of phase transitions

1978 ◽  
Vol 19 (3) ◽  
pp. 203-224 ◽  
Author(s):  
Colin J. Thompson
Keyword(s):  
Phase Transitions ◽  
Statistical Mechanics
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