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Register a new userEfficiency of molecular machines with continuous phase space
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We consider a molecular machine described as a Brownian particle diffusing in a tilted periodic potential. We evaluate the absorbed and released power of the machine as a function of the applied molecular and chemical forces, by using the fact that the times for completing a cycle in the forward and the backward direction have the same distribution, and that the ratio of the corresponding splitting probabilities can be simply expressed as a function of the applied force. We explicitly evaluate the efficiency at maximum power for a simple sawtooth potential. We also obtain the efficiency at maximum power for a broad class of 2-D models of a Brownian machine and find that loosely coupled machines operate with a smaller efficiency at maximum power than their strongly coupled counterparts.
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We investigate the efficiency of systems of molecular motors operating at maximum power. We consider two models of kinesin motors on a microtubule: for both the simplified and the detailed model, we find that the many-body exclusion effect enhances the efficiency at maximum power of the many-motor system, with respect to the single motor case. Remarkably, we find that this effect occurs in a limited region of the system parameters, compatible with the biologically relevant range.
We study the statistics of the efficiency in a class of isothermal cyclic machines with realistic coupling between the internal degrees of freedom. We derive, under fairly general assumptions, the probability distribution function for the efficiency. We find that the macroscopic efficiency is always equal to the most likely efficiency, and it lies in an interval whose boundaries are universal as they only depend on the input and output thermodynamic forces, and not on the details of the machine. The machine achieves the upper boundary of such an interval only in the limit of tight coupling. Furthermore, we find that the tight coupling limit is a necessary, yet not sufficient, condition for the engine to perform close to the reversible efficiency. The reversible efficiency is the least likely regardless of the coupling strength, in agreement with previous studies. By using a large deviation formalism we derive a fluctuation relation for the efficiency which holds for any number of internal degrees of freedom in the system.
We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.
We propose a physically-realisable biochemical device that is coupled to a biochemical reservoir of mutual information, fuel molecules and a chemical bath. Mutual information allows work to be done on the bath even when the fuel molecules appear to be in equilibrium; alternatively, mutual information can be created by driving from the fuel or the bath. The system exhibits diverse behaviour, including a regime in which the information, despite increasing during the reaction, enhances the extracted work. We further demonstrate that a modified device can function without the need for external manipulation, eliminating the need for a complex and potentially costly control.
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