arXiv subjects

A. M. Jayannavar

Publications and source records attributed to A. M. Jayannavar.

At least 55 records · Page 3Linked to original sources

arXiv2014

Exchange fluctuation theorems for a chain of interacting particles in presence of two heat baths

The exchange fluctuation theorem for heat exchanged between two systems at different temperatures, when kept in direct contact, has been investigated by C. Jarzynski and D. K. Wójcik, in Phys. Rev. Lett. {\bf 92}, 230602 (2004). We extend this result to the case where two Langevin reservoirs at different temperatures are connected via a conductor made of interacting particles, and are subjected to an external drive or work source. The Langevin reservoirs are characterized by Gaussian white noise fluctuations and concomitant friction coefficients. We first derive the Crooks theorem for the ratio between forward and reverse paths, and discuss the first law in this model. Then we derive the modified detailed fluctuation theorems (MDFT) for the heat exchanged at each end. These theorems differ from the usual form of the detailed fluctuation theorems (DFT) in literature, due the presence of an extra multiplicative factor. This factor quantifies the deviation of our MFDT from the DFT. Finally, we numerically study our model, with only two interacting particles for simplicity.

cond-mat.stat-mech↗

arXiv2014

Extracting work from a single heat bath - A case study on Brownian particle under external magnetic field in presence of information

Work can be extracted from a single bath beyond the limit set by the second law by performing measurement on the system and utilising the acquired information. As an example we studied a Brownian particle confined in a two dimensional harmonic trap in presence of magnetic field, whose position co-ordinates are measured with finite precision. Two separate cases are investigated in this study - (A) moving the center of the potential and (B) varying the stiffness of the potential. Optimal protocols which extremise the work in a finite time process are explicitly calculated for these two cases. For Case-A, we show that even though the optimal protocols depend on magnetic field, surprisingly, extracted work is independent of the field. For Case-B, both the optimal protocol and the extracted work depend on the magnetic field. However, the presence of magnetic field always reduces the extraction of work.

cond-mat.stat-mech↗

arXiv2014

Derivation of the not-so-common fluctuation theorems

The detailed fluctuation theorems of the exact form $P(A)/P(-A)=e^A$ exist only for a handful of variables $A$, namely for work (Crooks theorem), for total entropy change (Seifert's theorem), etc. However, the so-called modified detailed fluctuation theorems can be formulated for several other thermodynamic variables as well. The difference is that the modified relations contain an extra factor, which is dependent on $A$. This factor is usually an average of a quantity $e^{-B}$, where $B\neq A$, with repect to the conditional probability distribution $P(B|A)$. The corresponding modified integral fluctuation theorems also differ from their original counterparts, by not having the usual form $\left =1$. The generalization of these relations in presence of feedback has been discussed briefly. The results derived here serve to complement the already existing results in fluctuation theorems. The steps leading to the quantum version of these derivations have been outlined in the appendix.

cond-mat.stat-mech↗

arXiv2014

Fluctuation theorems for excess and housekeeping heats for underdamped systems

We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it naturally leads to the integral fluctuation theorem for housekeeping heat. We also derive the modified detailed fluctuation theorems for the excess and housekeeping heats.

cond-mat.stat-mech↗

arXiv2013

Fluctuation theorems in inhomogenious media under coarse graining

We compare the fluctuation relations for work and entropy in underdamped and overdamped systems, when the friction coefficient of the medium is space-dependent. We find that these relations remain unaffected in both cases. However, for the overdamped system, the analysis is more involved, and a blind application of normal rules of calculus would lead to inconsistent results.

cond-mat.stat-mech↗

arXiv2012

Fluctuation relations for heat engines in time-periodic steady states

A fluctuation relation for heat engines (FRHE) has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external parameters are changed cyclically, eventually bringing the system back to its initial state, once the coupling with the hot bath is switched off. In this work, we lift the condition of initial thermal equilibrium and derive a new fluctuation relation for the central system (heat engine) being in a time-periodic steady state (TPSS). Carnot's inequality for classical thermodynamics follows as a direct consequence of this fluctuation theorem even in TPSS. For the special cases of the absence of hot bath and no extraction of work, we obtain the integral fluctuation theorem for total entropy and the generalized exchange fluctuation theorem, respectively. Recently microsized heat engines have been realized experimentally in the TPSS. We numerically simulate the same model and verify our proposed theorems.

cond-mat.stat-mech↗

arXiv2012

Universal interpretation of efficacy parameter in perturbed nonequilibrium systems

The fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium, and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law. They have mainly been derived for a predetermined external drive applied to the system. However, to improve the efficiency of a process, one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system, during its evolution. In such a case, the forms of the conventional fluctuation theorems get modified, the correction term involving terms that depend on the way the reverse/conjugate process is defined, namely, the rules of using feedback in order to generate the exact time-reversed/conjugate protocols. We show in this paper that this can be done in a large number of ways, and in each case we would get a different expression for the correction terms. This would in turn lead to several lower bounds on the mean work that must be performed on the system, or on the entropy changes. Here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter, and find that this form gives rise to a lower bound for the mean work that retains a consistent physical meaning regardless of the design of feedback along the conjugate process, as opposed to the case of the previously mentioned form of the modified fluctuation theorems.

cond-mat.stat-mech↗

arXiv2012

Fluctuation theorems in presence of information gain and feedback

In this study, we rederive the fluctuation theorems in presence of feedback, by assuming the known Jarzynski equality and detailed fluctuation theorems. We first reproduce the already known work theorems for a classical system, and then extend the treatment to the other classical theorems. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system-bath coupling. However, it is assumed that the measurement process involves classical errors.

cond-mat.stat-mech↗

arXiv2012

Generalized entropy production fluctuation theorems for quantum systems

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

cond-mat.stat-mech↗

arXiv2011

Quantum Jarzynski Equality with multiple measurement and feedback for isolated system

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast to the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.

cond-mat.stat-mech↗

arXiv2011

The effect of confinement on stochastic resonance in continuous bistable systems

Using the input energy per cycle as a quantifier of stochastic resonance (SR), we show that SR is observed in superharmonic (hard) potentials. However, it is not observed in subharmonic (soft) potentials, even though the potential is bistable. These results are consistent with recent observations based on amplitude of average position as a quantifier. In both soft and hard potentials, we observe resonance phenomenon as a function of the driving frequency. The nature of probability distributions of average work are qualitatively different for soft and hard potentials.

cond-mat.stat-mech↗

arXiv2011

Stochastic Resonance in Periodic Potentials

The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of occurrence of SR in periodic potential systems is not conclusively resolved. Our present numerical work shows that the periodic potential system indeed exhibits SR in the high frequency regime, where the linear response theory yields maximum frequency dependent mobility as a function of noise strength. The existence of two (and only two) distinct dynamical states of trajectories in this moderately feebly-damped periodically driven noisy periodic potential system plays an important role in the occurrence of SR.

cond-mat.stat-mech↗

arXiv2010

Fluctuation theorems and atypical trajectories

In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities like the classical work ($W_c$), thermodynamic work ($W$), total entropy ($Δs_{tot}$) and dissipated heat ($Q$), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at macroscale. Nature of distributions for the thermodynamic work and the entropy production in nonlinear models may exhibit peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit peak in the regime of typical behaviour only.

cond-mat.stat-mech↗

arXiv2009

Yet another surprise in the problem of classical diamagnetism

The well known Bohr-van Leeuwen Theorem states that the orbital diamagnetism of classical charged particles is identically zero in equilibrium. However, results based on real space-time approach using the classical Langevin equation predicts non-zero diamagnetism for classical unbounded (finite or infinite) systems. Here we show that the recently discovered Fluctuation Theorems, namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly predict a free energy that depends on magnetic field as well as on the friction coefficient, in outright contradiction to the canonical equilibrium results. However, in the cases where the Langevin approach is consistent with the equilibrium results, the Fluctuation Theorems lead to results in conformity with equilibrium statistical mechanics. The latter is demonstrated analytically through a simple example that has been discussed recently.

cond-mat.stat-mech↗

arXiv2009

Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analyzed in terms of the average work done on the system per cycle. This is in contrast to the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyze the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.

cond-mat.stat-mech↗

arXiv2009

Entropy production theorems and some consequences

The total entropy production fluctuations are studied in some exactly solvable models. For these systems, the detailed fluctuation theorem holds even in the transient state, provided initially the system is prepared in thermal equilibrium. The nature of entropy production during the relaxation of a system to equilibrium is analyzed. The averaged entropy production over a finite time interval gives a better bound for the average work performed on the system than that obtained from the well known Jarzynski equality. Moreover, the average entropy production as a quantifier for information theoretic nature of irreversibility for finite time nonequilibrium processes is discussed.

cond-mat.stat-mech↗

arXiv2009

S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.

cond-mat.mes-hall↗

arXiv2008

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

We investigate the total entropy production of a Brownian particle in a driven bistable system. This system exhibits the phenomenon of stochastic resonance. We show that in the time-periodic steady state, the probability density function for the total entropy production satisfies Seifert's integral and detailed fluctuation theorems over finite time trajectories.

cond-mat.stat-mech↗