The Jarzynski relation (and its variants) has provided a route to the experimental evaluation of equilibrium free energy changes based on measurements conducted under arbitrary non-equilibrium conditions. Schroeder and co-workers [Soft Matter 10, 2178 (2014) and J. Chem. Phys. 141, 174903 (2014)] have recently exploited this fact to determine the elastic properties of model DNA from simulations and experiments of chain extension under elongational flow, bypassing the need to make these measurements mechanically using sophisticated optical trapping techniques. In this paper, motivated by these observations, we investigate chain elasticity analytically, using the Jarzynski relation and a finitely extensible nonlinear elastic-type Rouse model within a path integral formalism to calculate (essentially exactly) both the flow-induced free energy change between chain conformations of definite average end-to-end distance, as well as the force-extension curve that follows from it. This curve, based on a new analytic expression, matches the trends in the corresponding curve obtained from a model of chain stretching developed by Marko and Siggia [Macromolecules 28, 8759 (1995)], which itself is in very satisfactory agreement with the numerical and experimental data from the work of Schroeder et al.

A path integral approach used earlier to calculate the exact heat distribution function of a harmonically trapped Brownian oscillator at a fixed temperature (Chatterjee and Cherayil 2010 Phys. Rev. E 82 051104) is extended in this paper to a consideration of heat fluctuations in a dual temperature system. Our new calculations complement recent experimental data obtained by Ciliberto et al (2013 J. Stat. Mech. P12014) on the stochastic thermodynamics of an electrical circuit made up of coupled resistors maintained at two distinct temperatures. Measurements of various thermodynamic quantities in this system, including the heat, work and energy, reveal trends that represent interesting generalizations of results for the single temperature case. In particular, the measured distribution of the heat exchanged at one of the reservoirs is found to agree qualitatively with a fluctuation relation applicable at long times. In the present work, we exploit the formal equivalence between the electrical circuit and a system of coupled Brownian oscillators to derive, within the path integral formalism and for a special set of parameter values, an exact integral representation-valid for all times-of the total heat distribution function of the system. We find that the infinite-time limit of this distribution shows interesting departures from its expected behavior.

In an extension of earlier studies from this group on the application of the Jarzynski equality to the determination of the elastic properties of a finitely extensible Rouse model of polymers under flow [A. Ghosal and B. J. Cherayil, J. Chem. Phys. 144, 214902 (2016)], we derive several new theoretical results in this paper on the nature of the distribution function P(w) that governs the long-time limit t>>1 of the fluctuations in the work w performed by the polymer during flow-induced stretching. In particular, we show that an expression for the average of the nth power of the work, ⟨w(t)⟩, can be obtained in closed form in this limit, making it possible to exactly calculate three important statistical measures of P(w): the mean μ, the skewness γ, and the kurtosis γ (apart from the variance σ). We find, for instance, that to leading order in t, the mean grows linearly with t at a constant value of the dimensionless flow rate Wi and that the slope of the μ-t curve increases with increasing Wi. These observations are in complete qualitative agreement with data from Brownian dynamics simulations of flow-driven double-stranded DNA by Latinwo and Schroeder [Macromolecules 46, 8345 (2013)]. We also find that the skewness γ exhibits an interesting inversion of sign as a function of Wi, starting off at positive values at low Wi and changing to negative values at larger Wi. The inversion takes place in the vicinity of what we interpret as a coil-stretch transition. Again, the finding exactly reproduces behavior seen in other numerical and experimental work by the above group Latinwo et al. [J. Chem. Phys. 141, 174903 (2014)]. Additionally, at essentially the same value of Wi at which this sign inversion takes place, we observe that the kurtosis reaches a minimum, close to 1, providing further evidence of the existence of a coil-stretch transition at this location. Our calculations reproduce another numerical finding: a power law dependence on Wi of the rate of work production that is characterized by two distinct regimes, one lying below the putative coil-stretch transition, where the exponent assumes one value, and the other above, where it assumes a second.

A lower bound on the total entropy production rate is inferred from the time-irreversibility in partially observed and coarsed-grained systems operating far from equilibrium.

Face masks are used to intercept respiratory droplets to prevent spreading of air-borne diseases. Designing face masks with better efficiency needs microscopic understanding on how respiratory droplets move through a mask. Here we study a simple model on the interception of droplets by a face mask. The mask is treated as a polymeric network in an asymmetric confinement, while the droplet is taken as a micrometer sized tracer colloidal particle, subject to driving force that mimics the breathing. We study numerically, using the Langevin dynamics, the tracer particle permeation through the polymeric network. We show that the permeation is an activated process following an Arrhenius dependence on temperature. The potential energy profile responsible for the activation process increases with tracer size, tracer bead interaction, network rigidity and decreases with the driving force and confinement length. A deeper energy barrier led to better efficiency to intercept the tracer particles of a given size in the presence of driving force at room temperature. Our studies may help to design mask with better efficiency.