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Register a new userInconsistency of the non-standard definition of work
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We show that the recently postulated non-standard definition of work proportional to force variation rather than to displacement [A. Imparato and L. Peliti, cond-mat arXiv:0706.1134v1] is thermodynamically inconsistent at both microscopic and macroscopic scales and leads to non-physical results, including free energy changes that depend on arbitrary parameters.
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The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In the special case where the system dynamics can be described by a double-well potential with metastable and stable states, dynamics occurs in two stages: a fast relaxation to local equilibrium followed by a slow equilibration of populations in each coarse-grained state. We have recently observed the Mpemba effect experimentally in such a setting, for a colloidal particle immersed in water. Here, we show that this metastable Mpemba effect arises from a non-monotonic temperature dependence of the maximum amount of work that can be extracted from the local-equilibrium state at the end of Stage 1.
Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial H(x,t)/ partial t which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.
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.
We study the large deviations of the distribution P(W_tau) of the work associated with the propulsion of individual active brownian particles in a time interval tau, in the region of the phase diagram where macroscopic phase separation takes place. P(W_tau) is characterised by two peaks, associated to particles in the gaseous and in the clusterised phases, and two separate non-convex branches. Accordingly, the generating function of W_tau cumulants displays a double singularity. We discuss the origin of such non-convex branches in terms of the peculiar dynamics of the system phases, and the relation between the observation time tau and the typical persistence times of the particles in the two phases.
The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not previously been considered. Here, we present a Bayesian formalism for estimating free-energy changes from non-equilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise, and therefore provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with AFM, optical, and magnetic tweezers.
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