Equality connecting energy dissipation with violation of fluctuation-response relation

In systems driven away from equilibrium, the velocity correlation function and the linear response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under non-equilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Lett, v2: major revision, v3: minor revisio

Numerical simulations on Szilard's engine and information erasure

We present a computational model for Szilard's engine and the information discarding process. Taking advantage of a fact that the one is essentially the reversed cycle of the other, we can discuss the both by employing the same model. Through numerical simulations we calculate the work extracted by the engine and the heat generation in the information discarding process. It is found that these quantities depend on some realistic ingredients, which means that the work done by the engine is no longer canceled by the heat generation in the information erasure.Comment: 8 pages, 6 figures. submitted to Phys. Rev. Let

Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems

For Brownian motion of a single particle subject to a tilted periodic potential on a ring, we propose a formula for experimentally determining the cumulant generating function of time-averaged current without measurements of current fluctuations. We first derive this formula phenomenologically on the basis of two key relations: a fluctuation relation associated with Onsager's principle of the least energy dissipation in a sufficiently local region and an additivity relation by which spatially inhomogeneous fluctuations can be properly considered. We then derive the formula without any phenomenological assumptions. We also demonstrate its practical advantage by numerical experiments.Comment: 4 pages, 1 figure; In ver. 2, the organization of the paper has been revised. In ver. 3, substantial revisions have been don

Nonequilibrium dissipation-free transport in F1-ATPase and the thermodynamic role of asymmetric allosterism

F1-ATPase (or F1), the highly-efficient and reversible biochemical engine, has motivated physicists as well as biologists to imagine the design principles governing machines in the fluctuating world. Recent experiments have clarified yet another interesting property of F1; the dissipative heat inside the motor is very small, irrespective of the velocity of rotation and energy transport. Conceptual interest is devoted to the fact that the amount of internal dissipation is not simply determined by the sequence of equilibrium pictures, but also relies on the rotational-angular dependence of nucleotide affinity, which is a truly nonequilibrium aspect. We propose that the totally asymmetric allosteric model (TASAM), where adenosine triphosphate (ATP) binding to F1 is assumed to have low dependence on the angle of the rotating shaft, produces results that are most consistent with the experiment. Theoretical analysis proves the crucial role of two time scales in the model, which explains the universal mechanism to produce the internal dissipation-free feature. The model reproduces the characteristic torque dependence of the rotational velocity of F1, and predicts that the internal dissipation upon the ATP synthesis direction rotation becomes large at the low nucleotide condition.Comment: 10 pages, 5 figures + Supplementary Material (9 pages, 9 figures

Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality

On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics take place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition -an argued glassiness signature- to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. We fully characterize the finite-size properties of the order parameter across the first order transition