Papers by Robert Swendsen
Entropy
Two distinct puzzles, which are both known as Gibbs' paradox, have interested physicists since th... more Two distinct puzzles, which are both known as Gibbs' paradox, have interested physicists since they were first identified in the 1870s. They each have significance for the foundations of statistical mechanics and have led to lively discussions with a wide variety of suggested resolutions. Most proposed resolutions had involved quantum mechanics, although the original puzzles were entirely classical and were posed before quantum mechanics was invented. In this paper, I show that contrary to what has often been suggested, quantum mechanics is not essential for resolving the paradoxes. I present a resolution of the paradoxes that does not depend on quantum mechanics and includes the case of colloidal solutions, for which quantum mechanics is not relevant.
Entropy
The proper definition of thermodynamics and the thermodynamic entropy is discussed in the light o... more The proper definition of thermodynamics and the thermodynamic entropy is discussed in the light of recent developments. The postulates for thermodynamics are examined critically, and some modifications are suggested to allow for the inclusion of long-range forces (within a system), inhomogeneous systems with non-extensive entropy, and systems that can have negative temperatures. Only the thermodynamics of finite systems are considered, with the condition that the system is large enough for the fluctuations to be smaller than the experimental resolution. The statistical basis for thermodynamics is discussed, along with four different forms of the (classical and quantum) entropy. The strengths and weaknesses of each are evaluated in relation to the requirements of thermodynamics. Effects of order 1/N, where N is the number of particles, are included in the discussion because they have played a significant role in the literature, even if they are too small to have a measurable effect in an experiment. The discussion includes the role of discreteness, the non-zero width of the energy and particle number distributions, the extensivity of models with non-interacting particles, and the concavity of the entropy with respect to energy. The results demonstrate the validity of negative temperatures.
Thermodynamics of finite systems: a key issues review
Reports on progress in physics. Physical Society (Great Britain), 2018
A little over ten years ago, Campisi, and Dunkel and Hilbert, published papers claiming that the ... more A little over ten years ago, Campisi, and Dunkel and Hilbert, published papers claiming that the Gibbs (volume) entropy of a classical system was correct, and that the Boltzmann (surface) entropy was not. They claimed further that the quantum version of the Gibbs entropy was also correct, and that the phenomenon of negative temperatures was thermodynamically inconsistent. Their work began a vigorous debate of exactly how the entropy, both classical and quantum, should be defined. The debate has called into question the basis of thermodynamics, along with fundamental ideas such as whether heat always flows from hot to cold. The purpose of this paper is to sum up the present status-admittedly from my point of view. I will show that standard thermodynamics, with some minor generalizations, is correct, and the alternative thermodynamics suggested by Hilbert, Hänggi, and Dunkel is not. Heat does not flow from cold to hot. Negative temperatures are thermodynamically consistent. The small ...
American Journal of Physics
Physical Review B
The replica Monte Carlo simulation method and finite-size transfer-matrix method are used to stud... more The replica Monte Carlo simulation method and finite-size transfer-matrix method are used to study low-temperature properties of the kJ Ising spin glass in two dimensions. We find the spinglass susceptibility exponent y=5. 11+0.05 with a zero-temperature transition. The ground-state entropy so-0.071+0.007 by Monte Carlo simulation agrees well with previous transfer-matrix calculation, and the specific heat at low temperature has an asymptotic form 2-2J/(I(B T) c/kB=1. 3J /(kBT) e,w hich indicates an energy 2J as low-lying excitations. We show that the replica Monte Carlo method is much faster than standard annealing for finding ground states.
Acceleration and analysis methods in statistical physics
AIP Conference Proceedings
Physical review. E, 2017
We present a surprisingly simple approach to high-accuracy calculations of the critical propertie... more We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.
Physical Review Letters, Nov 24, 1986
Nonuniversal critical dynamics in MC simulations
Monte Carlo calculation of renormalized coupling parameters. I. d =2 Ising model
Phys Rev B, 1984
... par différentes transformations en espace réel du modèle de Ising à d=2, en utilisant une tec... more ... par différentes transformations en espace réel du modèle de Ising à d=2, en utilisant une technique développée récemment pour calculer les paramètres renormalisés de couplage à partir d'une simulation de Monte Carlo d'un ... Faire une nouvelle recherche Make a new search.
Markov Chain Monte Carlo Methods for Bayesian Analysis
Cluster Monte Carlo algorithms
Physica a Statistical Mechanics and Its Applications, Sep 1, 1990
The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts ... more The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example. Various generalizations are then reviewed and some applications are discussed. Two complete Fortran programs for the algorithms are provided.
Advances in Monte Carlo computer simulation
Since the invention of the Metropolis method in 1953, Monte Carlo methods have been shown to prov... more Since the invention of the Metropolis method in 1953, Monte Carlo methods have been shown to provide an efficient, practical approach to the calculation of physical properties in a wide variety of systems. In this talk, I will discuss some of the advances in the MC simulation of thermodynamics systems, with an emphasis on optimization to obtain a maximum of useful information.
Gibbs’ Paradox and the Definition of Entropy
ABSTRACT Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the en... more ABSTRACT Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting Boltzmann’s definition of the entropy, the violation of the second law is eliminated, the properties of colloids are correctly predicted, and Gibbs’ Paradox vanishes.
Exponent Inequalities at the Roughening Transition
Phys Rev Lett, 1977
ABSTRACT
A Comparison Between Adaptive Integration and Path-Sampling Methods for Calculating Free Energy Differences in Molecular Systems
... 3:54 PM–4:06 PM. Preview Abstract. Authors: F. Marty Ytreberg Daniel M. Zuckerman (University... more ... 3:54 PM–4:06 PM. Preview Abstract. Authors: F. Marty Ytreberg Daniel M. Zuckerman (University of Pittsburgh). ... The first approach is an adaptive integration Monte Carlo procedure which continually updates the free energy profile connecting the two states of interest. ...
Three-state antiferromagnetic Potts model : a Monte Carlo study
Physical Review B Condensed Matter, 1990
Critical exponents and marginality of the four-state Potts model: Monte Carlo renormalization group
Phys Rev B, 1981
ABSTRACT
Monte Carlo Renormalization Group and Ising Models with n>=2
Phys Rev Lett, 1979
ABSTRACT
A Tale of Two Chains: Experiences from a Collaboration Between Statisticians and Physicists
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Papers by Robert Swendsen