Fluctuation theorems in q-canonical ensembles

2021 ◽  
Vol 563 ◽  
pp. 125337
Author(s):  
Haridas Umpierrez ◽  
Sergio Davis
Keyword(s):  
Fluctuation Theorems ◽  
Canonical Ensembles

Statistical mechanics

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Statistical Mechanics ◽  
Potential Model ◽  
Quantum Corrections ◽  
Inhomogeneous Systems ◽  
Hard Constraints ◽  
Complex Liquids ◽  
Fluid Membranes ◽  
Dynamical Properties ◽  
Canonical Ensembles ◽  
Grand Canonical

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

scholarly journals Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 216 ◽  
Author(s):  
Jianjia Wang ◽  
Xichen Wu ◽  
Mingrui Li ◽  
Hui Wu ◽  
Edwin Hancock
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Ensemble Methods ◽  
Brain Regions ◽  
Fmri Data ◽  
Thermal Systems ◽  
Network Construction ◽  
Network Characteristics ◽  
Network Entropy ◽  
Canonical Ensembles

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes.

Coherent alloy phase separation: Differences in canonical and grand canonical ensembles

1997 ◽  
Vol 55 (21) ◽  
pp. 14222-14229 ◽  
Author(s):  
E. M. Vandeworp ◽  
Kathie E. Newman
Keyword(s):  
Phase Separation ◽  
Canonical Ensembles ◽  
Grand Canonical

scholarly journals By-passing fluctuation theorems

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 231
Author(s):  
Paul Boes ◽  
Rodrigo Gallego ◽  
Nelly H. Y. Ng ◽  
Jens Eisert ◽  
Henrik Wilming
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Thermodynamics ◽  
Many Body ◽  
Fluctuation Theorems ◽  
Macroscopic States ◽  
Many Body Systems ◽  
Highly Correlated ◽  
Positive Work ◽  
Thermodynamical Processes ◽  
Reduced State

Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be by-passed if one allows for the use of catalysts---additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.

Sign in / Sign up

Export Citation Format

Share Document