# Ergodic hypothesis in classical statistical mechanics

@article{Oliveira2007ErgodicHI, title={Ergodic hypothesis in classical statistical mechanics}, author={C'esar R. de Oliveira and Thiago Werlang}, journal={Revista Brasileira De Ensino De Fisica}, year={2007}, volume={29}, pages={189-201} }

An updated discussion on physical and mathematical aspects of the ergodic hypothesis in classical equilibrium statistical mechanics is presented. Then a practical attitude for the justification of the microcanonical ensemble is indicated. It is also remarked that the difficulty in proving the ergodic hypothesis should be expected.

## 28 Citations

### Quantum Thermodynamics and Canonical Typicality

- Physics
- 2017

We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version…

### Understanding the ergodic hypothesis via analogies

- Business
- 2013

This article proposes analogies in order to clarify some important features of the referred hypothesis, and perception that the same macroscopic property, i.

### Statistical Physics and Information Theory

- PhysicsFound. Trends Commun. Inf. Theory
- 2010

This chapter discusses the Random Energy Model and Random Coding, as well as analysis tools and Asymptotic Methods, and the physical interpretation of information measures.

### Geometry and Statistics of Ehrenfest dynamics

- Mathematics
- 2010

Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The…

### Statistics and Nosé formalism for Ehrenfest dynamics

- Mathematics
- 2011

Quantum dynamics (i.e. the Schrödinger equation) and classical dynamics (i.e. Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this…

### Ergodicity of one-dimensional systems coupled to the logistic thermostat

- Mathematics
- 2016

We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ:…

### Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Sampling

- Computer ScienceArXiv
- 2019

The proposed Quantum-Inspired Hamiltonian Monte Carlo algorithm (QHMC) allows a particle to have a random mass matrix with a probability distribution rather than a fixed mass, and proves the convergence property of QHMC and shows why such a randommass can improve the performance when the authors sample a broad class of distributions.

### 3 AN OBJECTIVISTACCOUNT OF PROBABILITIES IN STATISTICAL MECHANICS

- Psychology
- 2011

Hoefer (2007, p. 550) offers the opinion that ‘the vast majority of scientists using non-subjective probabilities overtly or covertly in their research feel little need to spell out what they take…

### AN OBJECTIVISTACCOUNT OF PROBABILITIES IN STATISTICAL MECHANICS

- Psychology
- 2011

Hoefer (2007, p. 550) offers the opinion that ‘the vast majority of scientists using non-subjective probabilities overtly or covertly in their research feel little need to spell out what they take…

### Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution

- Physics
- 2019

The Boltzmann distribution is one of the key equations of thermal physics and is widely used in machine learning as well. Here I derive a Boltzmann distribution in a simple pedagogical example using…

## References

SHOWING 1-10 OF 37 REFERENCES

### The concept of probability in statistical physics

- Mathematics
- 1999

Introduction 1. The Neo-Laplacian approach to statistical mechanics 2. Subjectivism and the Ergodic approach 3. The Haar measure 4. Measure and topology in statistical mechanics 5. Three solutions…

### Classical Statistical Mechanics

- Physics
- 1999

Statistical mechanics poses the problem of deducing macroscopic properties of matter from the atomic hypothesis. According to the hypothesis matter consists of atoms or molecules that move subject to…

### Why Gibbs Phase Averages Work--The Role of Ergodic Theory

- EconomicsPhilosophy of Science
- 1980

We propose an "explanation scheme" for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford…

### Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics

- PhysicsThe British Journal for the Philosophy of Science
- 1996

We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is…

### Boltzmann’s Ergodic Hypothesis, a Conjecture for Centuries?

- Mathematics
- 2000

An overview of the history of Ludwig Boltzmann’s more than one hundred year old ergodic hypothesis is given. The existing main results, the majority of which is connected with the theory of…

### Introduction to Ergodic Theory

- Mathematics
- 1977

Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time…

### Ergodicity, ensembles, irreversibility in Boltzmann and beyond

- Physics
- 1995

The contents of a not too well-known paper by Boltzmann are critically examined. The etymology of the word ergodic and its implications are discussed. A connection with the modern theory of Ruelle is…

### Statistical Mechanics: A Short Treatise

- Physics
- 1999

1. Classical Statistical Mechanics.- 2. Statistical Ensembles.- 3. Equipartition and Critique.- 4. Thermodynamic Limit and Stability.- 5. Phase Transitions.- 6. Coexistence of Phases.- 7. Exactly…

### Modern ergodic theory

- Physics
- 1973

The founding fathers of statistical mechanics, Boltzmann, Maxwell, Gibbs and Einstein, invented the concept of ensembles to describe equilibrium and nonequilibrium macroscopic systems. In trying to…

### Equilibrium States in Ergodic Theory

- Economics, Physics
- 1998

1. Simple examples of equilibrium states 2. Some basic ergodic theory 3. Entropy 4. Equilibrium states and pressure 5. Gibbs measures 6. Equilibrium states and derivatives Appendix: Background…