Related Experiment Video
Updated: May 16, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Current fluctuations in the weakly asymmetric exclusion process with open boundaries.
Mieke Gorissen1, Carlo Vanderzande
1Faculty of Sciences, Hasselt University, 3590 Diepenbeek, Belgium.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
The additivity principle accurately predicts current fluctuations in large systems. For the weakly asymmetric exclusion process (WASEP), this principle was validated using numerical methods, revealing no dynamical phase transitions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Non-equilibrium Systems
Background:
- The additivity principle simplifies calculations in large diffusive systems.
- Understanding current fluctuations is crucial in non-equilibrium statistical mechanics.
Purpose of the Study:
- To apply the additivity principle to the weakly asymmetric exclusion process (WASEP).
- To investigate current fluctuations and density profiles in finite systems.
- To validate the additivity principle and explore finite-size scaling theory.
Main Methods:
- Application of the additivity principle for large systems.
- Numerical calculation of the cumulant generating function using the density matrix renormalization group (DMRG) for finite systems.
Main Results:
- The additivity principle was successfully applied and validated against numerical results.
- Density profiles associated with rare currents were calculated.
- No evidence of a dynamical phase transition was found in the WASEP.
Conclusions:
- The additivity principle is a valid tool for analyzing current fluctuations in the WASEP.
- The study provides insights into finite-size scaling for current fluctuations.
- The WASEP does not exhibit a dynamical phase transition under the studied conditions.
Related Concept Videos
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:25Boundary Conditions for Current Density
Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
01:16Electrostatic Boundary Conditions
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:19Cyclic Processes And Isolated Systems
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
01:27Electrostatic Boundary Conditions in Dielectrics
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.