Work relation in instantaneous-equilibrium transition of forward and reverse processes

Abstract

Realizing quasistatic processes in finite times requires additional control parameters to keep the system in instantaneous equilibrium (ieq). However, the finite-rate ieq transition of the reverse process is not just the time-reversal of the ieq forward process due to the odd-parity of controlling parameters. We theoretically show a work relation that the dissipated work of the ieq transition of the forward process is the same as that of the corresponding reverse process. The work relation can be interpreted as a generalization of equilibrium (quasistatic) processes. The work relation and the associated statistics of nonequilibrium work are experimentally confirmed in three different Brownian systems: the time-varying harmonic and non-harmonic potentials and the Brownian harmonic transport, which are manipulated by the optical feedback trap.

Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process

“…To realize the finite-time heat engine, independent control of temperature and potential is essential for constructing transition paths in engine cycles. The ieq of the isothermal process has already been implemented [33,34] in colloid experiments while realizing ieq protocols involving heating and cooling is challenging. With the protocols of time-dependent potential and temperature considered in this paper, it is possible to realize an ieq of isentropic or zero EP process.…”

“…For stochastic systems, it is possible to achieve a finite-rate transition between two designated equilibrium states [27,28] via a non-equilibrium path, and also to reduce the dissipated work [29]. Another recent advance is the shortcut-to-isothermality (ScI) transition [30,31] in which instantaneous equilibrium (ieq) at a fixed temperature is maintained at all moments during the finite speed transition, which was demonstrated experimentally in a Brownian particle under a moving harmonic potential [32] and trapping potentials of varying stiffness [33,34]. The ScI transition manifests the idea of instantaneous equilibrium which generalizes the notion of equilibrium, and a work relation for the symmetry of the ScI of forward and reverse processes was established [13].…”

Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model

“…Very recently, thermodynamic uncertainty relations bounding the signal to noise ratio of a measured current have been also discovered [15]. In particular, the study of work and heat fluctuations has been the object of focus in several systems, such as overdamped linear Langevin Equation [16], particle diffusion in time-dependent potentials [17][18][19][20][21][22], Brownian particles driven by correlated forces [23], general thermal systems [24], asymmetric processes [25], underdamped Langevin Equation [26], or in transient relaxation dynamics [27]. The interest in these quantities is motivated by the search for optimization protocols in models of stochastic engines or, from a more theoretical perspective, by the general symmetry properties or by singular behaviors that work and heat distributions can show [28].…”

Geodesic path for the minimal energy cost in shortcuts to isothermality

“…Shortcut to isothermality was proposed as a finitetime driving strategy to steer the system evolving along the path of instantaneous equilibrium states [9]. The strategy has been applied in reducing transition time between equilibrium states [10][11][12], improving the efficiency of free-energy estimation [13], constructing finitetime heat engines [14][15][16], and controlling biological evolutions [4,5]. The cost of the finite-time operation is the additional energy cost due to irreversibility posted by the fundamental thermodynamic law.…”