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Register a new userHeat and work distributions for mixed Gauss-Cauchy process
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We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $alpha=2$ and $alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system.
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For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with one degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions, and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.
The asymptotic tails of the probability distributions of thermodynamic quantities convey important information about the physics of nanoscopic systems driven out of equilibrium. We apply a recently proposed method to analytically determine the asymptotics of work distributions in Langevin systems to an one-dimensional model of single-molecule force spectroscopy. The results are in excellent agreement with numerical simulations, even in the centre of the distributions. We compare our findings with a recent proposal for an universal form of the asymptotics of work distributions in single-molecule experiments.
The paper discusses the natural emergence of directed motion in a dimer system due to a structural symmetry breaking. A generalised solution is obtained for the transport of such a system which is driven entirely by bath fluctuations. The result shows the existence of possibility of ratcheting driven by bath fluctuations. If this component of energy conversion driven by bath is taken into account the high efficiency of molecular motors as opposed to paradigmatic ratcheting models can probably be explained.
Macroscopic models which distinguish the longitudinal and transverse temperatures can provide improved descriptions of the microscopic shock structures as revealed by molecular dynamics simulations. Additionally, we can include three relaxation times in the models, two based on Maxwells viscoelasticity and its Cattaneo-equation analog for heat flow, and a third thermal, based on the Krook-Boltzmann equation. This approach can replicate the observed lags of stress (which lags behind the strain rate) and heat flux (which lags behind the temperature gradient), as well as the eventual equilibration of the two temperatures. For profile stability the time lags cannot be too large. By partitioning the longitudinal and transverse contributions of work and heat and including a tensor heat conductivity and bulk viscosity, all the qualitative microscopic features of strong simple-fluid shockwave structures can be reproduced.
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines. We also find estimates for the time-dependent thresholds that the stochastic work does not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results, which entail an extension of martingale theory for entropy production, are tested with numerical simulations of a stochastic photoelectic device.
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