Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLangevin equation in systems with also negative temperatures
115
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We discuss how to derive a Langevin equation (LE) in non standard systems, i.e. when the kinetic part of the Hamiltonian is not the usual quadratic function. This generalization allows to consider also cases with negative absolute temperature. We first give some phenomenological arguments suggesting the shape of the viscous drift, replacing the usual linear viscous damping, and its relation with the diffusion coefficient modulating the white noise term. As a second step, we implement a procedure to reconstruct the drift and the diffusion term of the LE from the time-series of the momentum of a heavy particle embedded in a large Hamiltonian system. The results of our reconstruction are in good agreement with the phenomenological arguments. Applying the method to systems with negative temperature, we can observe that also in this case there is a suitable Langevin equation, obtained with a precise protocol, able to reproduce in a proper way the statistical features of the slow variables. In other words, even in this context, systems with negative temperature do not show any pathology.
rate research
Read More
We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schrodinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble inequivalence, this phase is thermodynamically stable only in the microcanonical ensemble. In particular, we obtain an explicit expression of the microcanonical entropy close to the transition line, located at infinite temperature. This task is accomplished making use of large-deviation techniques, that allow us to compute, in the limit of large system size, also the subleading corrections to the microcanonical entropy. These subleading terms are crucial ingredients to account for the first-order mechanism of the transition, to compute its order parameter and to predict the existence of negative temperatures in the localized phase. All of these features can be viewed as signatures of a thermodynamic phase where the translational symmetry is broken spontaneously due to a condensation mechanism yielding energy fluctuations far away from equipartition: actually they prefer to participate in the formation of nonlinear localized excitations (breathers), typically containing a macroscopic fraction of the total energy.
In a recent paper, Dunkel and Hilbert [Nature Physics 10, 67-72 (2014)] use an entropy definition due to Gibbs to provide a consistent thermostatistics which forbids negative absolute temperatures. Here we argue that the Gibbs entropy fails to satisfy a basic requirement of thermodynamics, namely that when two bodies are in thermal equilibrium, they should be at the same temperature. The entropy definition due to Boltzmann does meet this test, and moreover in the thermodynamic limit can be shown to satisfy Dunkel and Hilberts consistency criterion. Thus, far from being forbidden, negative temperatures are inevitable, in systems with bounded energy spectra.
We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modeling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can be also somewhat alternative to each other, e.g., Continuous Time Random Walk (CTRW) and Fractional Brownian Motion (FBM). To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modeling of velocity dynamics. The complexity of the medium is parameterized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particles dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while anti-persistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for non-thermal fractional Brownian motion with reflecting walls, and we discuss broader implications.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
