• Corpus ID: 117841752

Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics

@inproceedings{Ruelle2004ThermodynamicFT,
  title={Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics},
  author={David Ruelle},
  year={2004}
}
  • D. Ruelle
  • Published 29 November 2004
  • Economics, Mathematics
1. Introduction to the 2nd edition 2. Introduction 3. Theory of Gibbs States 4. Gibbs States: complements 5. Translation invariance: theory of equilibrium states 6. Connection between Gibbs States and equilibrium 7. One-dimensional systems 8. Extension of the thermodynamic formalism Appendix A.1. Miscellaneous definitions and results Appendix A.2. Topological dynamics Appendix A.3. Convexity Appendix A.4. Measures and abstract dynamical systems Appendix A.5. Integral representations on convex… 
Ju l 2 02 0 PRESSURE AND EQUILIBRIUM STATES IN ERGODIC
  • Chemistry
  • 2021
1. Definition of the Subject and Its Importance 2 2. Introduction 2 3. Warming Up: Thermodynamic Formalism for Finite Systems 4 4. Shift spaces, Invariant Measures and Entropy 7 5. The Variational
Entropic fluctuations in statistical mechanics: I. Classical dynamical systems
Within the abstract framework of dynamical system theory we describe a general approach to the transient (or Evans–Searles) and steady state (or Gallavotti–Cohen) fluctuation theorems of
Foundations of Ergodic Theory
Preface 1. Recurrence 2. Existence of invariant measures 3. Ergodic theorems 4. Ergodicity 5. Ergodic decomposition 6. Unique ergodicity 7. Correlations 8. Equivalent systems 9. Entropy 10.
Geometrical constructions of equilibrium states
In this note we report some advances in the study of thermodynamic formalism for a class of partially hyperbolic systems—center isometries—that includes regular elements in Anosov actions. The
Pressure and Equilibrium States in Ergodic Theory
Our goal is to present the basic results on one-dimensional Gibbs and equilibrium states viewed as special invariant measures on symbolic dynamical systems, and then to describe without
Stochastic Processes and Statistical Mechanics
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous
Equilibrium States in Negative Curvature
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework
Thermodynamic Limit in Statistical Physics
TLDR
The major aim of this work is to provide a better qualitative understanding of the physical significance of the thermodynamic limit in modern statistical physics of the infinite and "small" many-particle systems.
Perspectives on Statistical Thermodynamics
This original text develops a deep, conceptual understanding of thermal physics, highlighting the important links between thermodynamics and statistical physics, and examining how thermal physics
On the relationship of energy and probability in models of classical statistical physics
TLDR
A new point of view on the mathematical foundations of statistical physics of infinite volume systems is presented, based on the newly introduced notions of transition energy function, transition energy field and one-point transitionEnergy field, which establishes a straightforward relationship between the probabilistic notion of (Gibbs) random field and the physical notion of(transition) energy.
...
...

References

SHOWING 1-10 OF 64 REFERENCES
Statistical Mechanics: Rigorous Results
Thermodynamic behaviour - ensembles the thermodynamic limit for thermodynamic functions - lattice systems the thermodynamic limit for thermodynamic functions - continuous systems low density
Mean entropy of states in classical statistical mechanics
The equilibrium states for an infinite system of classical mechanics may be represented by states over AbelianC* algebras. We consider here continuous and lattice systems and define a mean entropy
A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule
It is shown that for an infinite lattice system, thermodynamic equilibrium is the solution of a variational problem involving a mean entropy of states introduced earlier [2]. As an application, a
Statistical mechanics of quantum spin systems. III
AbstractIn the algebraic formulation the thermodynamic pressure, or free energy, of a spin system is a convex continuous functionP defined on a Banach space $$\mathfrak{B}$$ of translationally
Statistical mechanics of a one-dimensional lattice gas
We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase
Two remarks on extremal equilibrium states
First it is shown that each extremal equilibrium state is representable as limit of Gibbs states in finite volumes, and that an analogous statement holds for extremal invariant equilibrium states.
A Relativised Variational Principle for Continuous Transformations
The formula (1.1) also follows from (1.2). Actually we prove a more general relative variational principle by considering pressure instead of entropy, and this result generalises the variational
Observables at infinity and states with short range correlations in statistical mechanics
We say that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a
A heuristic theory of phase transitions
LetZ be a suitable Banach space of interactions for a lattice spin system. Ifn+1 thermodynamic phases coexist for Φ0 ∈Z, it is shown that a manifold of codimensionn of coexistence of (at least)n+1
...
...