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Statistical mechanics is the third pillar of modern physics, next to quantum theory and relativity theory. It aims to account for the behaviour of macroscopic systems in terms of the dynamical laws that govern their microscopic constituents and probabilistic assumptions about them. In this Element, the authors investigate the philosophical and foundational issues that arise in SM. The authors introduce the two main theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. In doing so, the authors examine how probabilities are introduced into the theories, how they deal with irreversibility, how they understand the relation between the micro and the macro level, and how the two approaches relate to each other. Throughout, the authors also pinpoint open problems that can be subject of future research. This title is also available as Open Access on Cambridge Core.
Cover
Title page
Copyright page
Foundations of Statistical Mechanics
ntroduction
The Aims of Statistical Mechanics
The Theoretical Landscape of SM
Outline
Mechanics and Probability
Dynamical Systems
Hamiltonian Mechanics
Time-Reversal Invariance
Poincaré Recurrence
Ergodicity
Probability Theory
Points of Contact
Boltzmannian Statistical Mechanics
The Bare Bones of BSM
Defining Equilibrium: The Combinatorial Argument
The Approach to Equilibrium: The Ergodic Account
Two Objections: Loschmidt and Zermelo
The Residence Time Account
Typicality
Where Have Probabilities Gone?
Conditional Probabilities and the Mentaculus
Open Problems
Gibbsian Statistical Mechanics
A Primer on GSM
Articulating AP: Ergodicity
Probabilism
Articulating AP: Fluctuations
GSM and the Approach to Equilibrium
Coarse-Graining
Interventionism
The Epistemic Account
The Relation between GSM and BSM
Open Questions for GSM
References
Acknowledgements