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The study of microsystems and the development of nanotechnologies require new techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Amongst the challenges, there is the need to deal with the…
We demonstrate how the ineluctable presence of thermal noise alters the measurement of forces acting on microscopic and nanoscopic objects. We quantify this effect exemplarily for a Brownian particle near a wall subjected to gravitational…
The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…
Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of…
The paper is devoted to the problem of the determination of regular and thermal forces acting on microscopic and smaller objects in fluids. One of the methods how regular forces are determined is the measurement of the drift velocity of…
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…
In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a colloidal particle near a wall in the presence of a gravitational field for which they study the influence of noise on the measurement of force. Their central…
The famous It\^o-Stratonovich dilemma arises when one examines a dynamical system with a multiplicative white noise. In physics literature, this dilemma is often resolved in favour of the Stratonovich prescription because of its two…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic…
We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…
Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called…
We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced…
In this work we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble…
We study transport of an inertial Brownian particle moving in a symmetric and periodic one-dimensional potential, and subjected to both a symmetric, unbiased external harmonic force as well as biased dichotomic noise $\eta(t)$ also known as…
We study a noisy drive mechanism for efficiency enhancement of Brownian motors operating on the micro-scale domain. It was proven [J. Spiechowicz et al., J. Stat. Mech. P02044, (2013)] that biased noise $\eta(t)$ can induce normal and…
We study the coherence of transport of an overdamped Brownian particle in frictional ratchet system in the presence of external Gaussian white noise fluctuations. The analytical expressions for the particle velocity and diffusion…
Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…
The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of non-equilibrium thermodynamical equalities as generalization of the…
The relativistic generalization of the Brownian motion is discussed. We show that the transformation property of the noise term is determined by requiring for the equilibrium distribution function to be Lorentz invariant, such as the…