Some Recent Advances in Classical Statistical Mechanics

Cohen, E. G. D.

doi:10.1007/3-540-46122-1_2

Cited by 7 publications

(7 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Fig. 7 the tails of the p(u) are plotted versus u, where Re = 540,000 is taken [16]. (b) These values of q decrease with r and increase with Re (cf.…”

Section: Simple Beck Theory [816]mentioning

confidence: 98%

“…Beck [8,16] has proposed a more complicated theory for the data of the Lewis and Swinney experiments, taking into account (a) a non-linear force term [−γ(∂V(|u|)/∂u)] with V(|u|) ∼ |u| 2α in the Langevin equation 4 and (b) adding a deterministic chaotic force term to the Langevin equation, which has a "universal" form and can account Table 3 [17]. for the observed slight skewness of the u-fluctuations in p(u).…”

Section: Refined Beck Theorymentioning

confidence: 99%

See 1 more Smart Citation

Superstatistics

Cohen

2004

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Einstein repeatedly criticized Boltzmann's statistics S(E) = k B log W(E) on the grounds that the probabilities W(E) to find a system in an energy state E should in principle follow a posteriori from its dynamics and not be postulated a priori. This implied the possible existence of other classical statistics than that of Boltzmann the first of which was proposed by Tsallis. In this paper, we discuss a class of generalized Boltzmann statistics: "superstatistics", developed by Beck and myself, which can be seen as a statistics of a statistics and contains Tsallis and other statistics as well. All these superstatistics appear to occur in systems with complicated dynamics, have non-additive and non-extensive entropies and apply in general to non-equilibrium systems. Two very accurate experiments will be discussed both done in fully developed turbulent circular Couette flow: one by La Porta et al. on the fluctuations of the acceleration of a tracer particle, the other by Lewis and Swinney for the fluctuations of the longitudinal velocity.

show abstract

“…In Fig. 7 the tails of the p(u) are plotted versus u, where Re = 540,000 is taken [16]. (b) These values of q decrease with r and increase with Re (cf.…”

Section: Simple Beck Theory [816]mentioning

confidence: 98%

Section: Refined Beck Theorymentioning

confidence: 99%

Superstatistics

Cohen

2004

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Such independence breaks down in small systems due to the contribution of fluctuations which depend on the type of statistical ensemble considered (e.g for the case of a stretched polymer [377]). The search for a new thermodynamic description of small systems has given rise to microcanonical ensemble theory of phase transitions [378] and new classical statistics such as that embodied in Tsallis-entropy [379] and Beck's theory [380] (for a review see [381]). From the current point of view, the most important aspect of biomolecular complexes is that they operate far from equilibrium, yet the possible relationship between nonequilibrium behavior and biological function is still unknown.…”

Section: Tests Of Nonequilibrium Theories In Statistical Physicsmentioning

confidence: 99%

Single-molecule experiments in biological physics: methods and applications

Ritort

2006

J. Phys.: Condens. Matter

389

463

View full text Add to dashboard Cite

Abstract. I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques.

show abstract

“…Since their discovery in the mid 90's [26,27,28] there has been a growing interest to elucidate their importance and implications. FTs provide a fresh look to our understanding of old questions such as the origin of irreversibility and the second law in statistical mechanics [29,30]. In addition, FTs provide statements about energy fluctuations in small systems which, under generic conditions, should be experimentally observable.…”

Section: Fluctuation Theorems (Fts)mentioning

confidence: 99%

Nonequilibrium Fluctuations in Small Systems: From Physics to Biology

Ritort

2007

Advances in Chemical Physics

181

217

View full text Add to dashboard Cite

In this paper I am presenting an overview on several topics related to nonequilibrium fluctuations in small systems. I start with a general discussion about fluctuation theorems and applications to physical examples extracted from physics and biology: a bead in an optical trap and single molecule force experiments. Next I present a general discussion on path thermodynamics and consider distributions of work/heat fluctuations as large deviation functions. Then I address the topic of glassy dynamics from the perspective of nonequilibrium fluctuations due to small cooperatively rearranging regions. Finally, I conclude with a brief digression on future perspectives.

show abstract

Some Recent Advances in Classical Statistical Mechanics

Cited by 7 publications

References 19 publications

Superstatistics

Superstatistics

Single-molecule experiments in biological physics: methods and applications

Nonequilibrium Fluctuations in Small Systems: From Physics to Biology

Contact Info

Product

Resources

About