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Register a new userJarzynski equality for superconducting optical cavities: an alternative path to determine Helmholtz free energy
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A superconducting cavity model was proposed as a way to experimentally investigate the work performed in a quantum system. We found a simple mathematical relationship between the free energy variation and visibility measurement in quantum cavity context. If we consider the difference of Hamiltonian at time $t_0$ and $t_lambda$ (protocol time) as a quantum work, then the Jarzynski equality is valid and the visibility can be used to determine the work done on the cavity.
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Measuring the fluctuations of work in coherent quantum systems is notoriously problematic. Aiming to reveal the ultimate source of these problems, we demand of work measurement schemes the sheer minimum and see if those demands can be met at all. We require ($mathfrak{A}$) energy conservation for arbitrary initial states of the system and ($mathfrak{B}$) the Jarzynski equality for thermal initial states. By energy conservation we mean that the average work must be equal to the difference of initial and final average energies, and that untouched systems must exchange deterministically zero work. Requirement $mathfrak{B}$ encapsulates the second law of thermodynamics and the quantum--classical correspondence principle. We prove that work measurement schemes that do not depend on the systems initial state satisfy $mathfrak{B}$ if and only if they coincide with the famous two-point measurement scheme, thereby establishing that state-independent schemes cannot simultaneously satisfy $mathfrak{A}$ and $mathfrak{B}$. Expanding to the realm of state-dependent schemes allows for more compatibility between $mathfrak{A}$ and $mathfrak{B}$. However, merely requiring the state-dependence to be continuous still effectively excludes the coexistence of $mathfrak{A}$ and $mathfrak{B}$, leaving the theoretical possibility open for only a narrow class of exotic schemes.
We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.
The free energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum energy path directly on the free energy surface (FES) at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free energy gradient for a given RC. These derivatives are then used to find the actual minimum energy reaction path at finite temperature, in a way similar to the Intrinsic Reaction Path of Fukui on the potential energy surface [K Fukui J. Phys. Chem. 74, 4161 (1970)]. Once the path is know, one can calculate the free energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum free energy path at 300 K for the addition of the 1,1-dichlorocarbene to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.
We discuss and qualify a previously unnoticed connection between two different phenomena in the physics of nanoscale friction, general in nature and also met in experiments including sliding emu- lations in optical lattices, and protein force spectroscopy. The first is thermolubricity, designating the condition in which a dry nanosized slider can at sufficiently high temperature and low velocity exhibit very small viscous friction f ~ v despite strong corrugations that would commonly imply hard mechanical stick-slip f ~ log(v). The second, apparently unrelated phenomenon present in externally forced nanosystems, is the occurrence of negative work tails (free lunches) in the work probabilty distribution, tails whose presence is necessary to fulfil the celebrated Jarzynski equality of non-equilibrium statistical mechanics. Here we prove analytically and demonstrate numerically in the prototypical classical overdamped one-dimensional point slider (Prandtl-Tomlinson) model that the presence or absence of thermolubricity is exactly equivalent to satisfaction or violation of the Jarzynski equality. The divide between the two regimes, satisfaction of Jarzynski with ther- molubricity, and violation of both, simply coincides with the total frictional work per cycle falling below or above kT respectively. This concept can, with due caution, be extended to more complex sliders, thus inviting crosscheck experiments, such as searching for free lunches in cold ion sliding as well as in forced protein unwinding, and alternatively checking for a thermolubric regime in dragged colloid monolayers. As an important byproduct, we derive a parameter-free formula expressing the linear velocity coefficient of frictional dissipated power in the thermolubric viscous regime, correcting previous empirically parametrized expressions.
Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both, the classical and the quantum context. While the approaches and settings greatly differ from one to another, they all appear to rely on the initial state being a thermal Gibbs state. Here, we present an investigation of work distributions in driven isolated quantum systems, starting off from pure states that are close to energy eigenstates of the initial Hamiltonian. We find that, for the nonintegrable system in quest, the Jarzynski equality is fulfilled to good accuracy.
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