اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدJarzynski equality for the Jepsen gas
119
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
One particle in a classical perfect gas is driven out of equilibrium by changing its mass over a short time interval. The work done on the driven particle depends on its collisions with the other particles in the gas. This model thus provides an exam
ple of a non-equilibrium process in a system (the driven particle) coupled to an environment (the rest of the gas). We calculate the work done on the driven particle and compare the results to Jarzynskis equality relating a non-equilibrium work process to an equilibrium free-energy difference. The results for this model are generalised to the case of a system that is driven in one degree of freedom while interacting with the environment through other degrees of freedom.
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 spectro
scopy. 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.
A single bit memory system is made with a brownian particle held by an optical tweezer in a double-well potential and the work necessary to erase the memory is measured. We show that the minimum of this work is close to the Landauers bound only for v
ery slow erasure procedure. Instead a detailed Jarzynski equality allows us to retrieve the Landauers bound independently on the speed of this erasure procedure. For the two separated subprocesses, i.e. the transition from state 1 to state 0 and the transition from state 0 to state 0, the Jarzynski equality does not hold but the generalized version links the work done on the system to the probability that it returns to its initial state under the time-reversed procedure.
We have experimentally checked the Jarzynski equality and the Crooks relation on the thermal fluctuations of a macroscopic mechanical oscillator in contact with a heat reservoir. We found that, independently of the time scale and amplitude of the dri
ving force, both relations are satisfied. These results give credit, at least in the case of Gaussian fluctuations, to the use of these relations in biological and chemical systems to estimate the free energy difference between two equilibrium states. An alternative method to estimate of the free nergy difference in isothermal process is proposed too.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
