Heat fluctuations for underdamped Langevin dynamics

Abstract

Fluctuation theorems play a central role in nonequilibrium physics and stochastic thermodynamics. Here we derive an integral fluctuation theorem for the dissipated heat in systems governed by an underdamped Langevin dynamics. We show that this identity may be used to predict the occurrence of extreme events leading to exponential tails in the probability distribution functions of the heat and related quantities.

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

“…In consequence, while the three observables βW t , βQ t , and Σ t have the same expectation value, their LDFs may differ. In some circumstances, large fluctuations of the boundary terms may even induce a discontinuity of the SCGF at λ = 1, as pointed out recently [28]: the asymptotic expression ( 12) is then no longer valid and µ A (1) = µ(1). We shall see later on that this is very much dependent on the time delay.…”

“…and the exponential factors e ± γ 2m t come from the Jacobians of the transformations ξ(t) → x(t) associated with the two Langevin dynamics (see [30] or the supplemental material of [28] for a derivation). As usual, the continuous-time integrals in Eqs.…”

Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model

“…Very recently, thermodynamic uncertainty relations bounding the signal to noise ratio of a measured current have been also discovered [15]. In particular, the study of work and heat fluctuations has been the object of focus in several systems, such as overdamped linear Langevin Equation [16], particle diffusion in time-dependent potentials [17][18][19][20][21][22], Brownian particles driven by correlated forces [23], general thermal systems [24], asymmetric processes [25], underdamped Langevin Equation [26], or in transient relaxation dynamics [27]. The interest in these quantities is motivated by the search for optimization protocols in models of stochastic engines or, from a more theoretical perspective, by the general symmetry properties or by singular behaviors that work and heat distributions can show [28].…”

Heat Distribution of Relativistic Brownian Motion

“…Heat is a fundamental quantity in Stochastic Thermodynamics, i.e., the energy naturally exchanged between the system and the surrounding, in a disordered way. As a random variable, characterization of the statistics of heat for diffusive systems was carried in many different models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. These works bring physical insights into the thermodynamics of classical diffusive systems, however, as far as we known, they only deals with nonrelativistic systems.…”