arXiv subjects

Shubhashis Rana

Publications and source records attributed to Shubhashis Rana.

15 recordsLinked to original sources

arXiv2020

Precision and dissipation of a stochastic Turing pattern

Spontaneous pattern formation is a fundamental scientific problem that has received much attention since the seminal theoretical work of Turing on reaction-diffusion systems. In molecular biophysics, this phenomena often takes place under the influence of large fluctuations. It is then natural to inquire about the precision of such pattern. In particular, spontaneous pattern formation is a nonequilibrium phenomenon, and the relation between the precision of a pattern and the thermodynamic cost associated with it remains unexplored. Here, we analyze this relation with a paradigmatic stochastic reaction-diffusion model, the Brusselator in one spatial dimension. We find that the precision of the pattern is maximized for an intermediate thermodynamic cost, i.e., increasing the thermodynamic cost beyond this value makes the pattern less precise. Even though fluctuations get less pronounced with an increase in thermodynamic cost, we argue that larger fluctuations can also have a positive effect on the precision of the pattern.

cond-mat.stat-mech↗

arXiv2019

Tuning Self Organization Of Confined Active Particles By Steepness Of The Trap

We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They are also interacting with each other by a soft, isotropic, excluded-volume interaction. Particles are confined in a circular trap. The steepness of the trap is tuneable. Their average packing fraction and strength of rotational fluctuation are low. When the trap is steep, particles flock along its boundary. They form polar cluster that spreads over the boundary. The cluster has no spatial or structural order. We show, when the steepness is decreased beyond a threshold value, the clusters become round, compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order within them. We investigate kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the clusters need to roll around their centre of mass, to be spatially ordered. We also discuss the stability of the order when the trap is suddenly switched off.

cond-mat.soft↗

arXiv2018

Current reversal in interacting colloids under time-periodic drive

Using molecular dynamics simulations, we study particle-transport in a system of interacting colloidal particles on a ring, where the system is driven by a time-dependent external potential, moving along the ring. We consider two driving protocols: (i) the external potential barrier moves with a uniform velocity $v$ along the ring, and (ii) it moves in discrete jumps with jump-length $l$ and waiting time $τ$ with an effective velocity $v=l/τ$. The time-averaged (dc) particle current, which always remains positive in case (i), interestingly reverses its direction in case (ii) upon tuning the particle-number density $ρ_0$ and the effective barrier velocity $v$. We also find a scaling form for the current in terms of number density, barrier velocity, barrier height and temperature of the system.

cond-mat.stat-mech↗

arXiv2018

Second law for an autonomous information machine connected with multiple baths

In an Information machine system's dynamics gets affected by the attached information reservoir. Second law of thermodynamics can be apparently violated for this case. In this article we have derived second law for an information machine, when the system is connected to multiple heat baths along with a work source and a single information reservoir. Here a sequence of bits written on a tape is considered as an information reservoir. We find that the bath entropy production during a time interval is restricted by the change of Shannon entropy of the composite system (system + information reservoir) during that interval. We have also given several examples where this law can be applicable and shown that our bound is tighter.

cond-mat.stat-mech↗

arXiv2016

Second law, Landauer's Principle and Autonomous information machine

Second law of thermodynamics can be apparently violated for systems whose dynamics depends on acquired information by measurement. However, when one consider measurement and erasure process together along with the system it saves the second law. We consider a simple example of information machine where information is used as a resource to increase its performance. The system is connected to two baths, a work source and a moving tape which is used as an information reservoir. The performance of the device is autonomous. The system acts as an engine, erasure or refrigerator. Even combination of any two is possible. All these possibilities are allowed by generalized second law.

cond-mat.stat-mech↗

arXiv2016

A multipurpose information engine that can go beyond the Carnot limit

Motivated by the recent work by Mandal and Jarzynski on autonomous Maxwell demon information engine, we have extended their model by introducing two different heat baths. The system (demon) is coupled to a memory register (tape) and a work source. The performance of the system depends on the interplay between these two sources along with the heat baths. We have found the system can act as an engine, refrigerator or an eraser. Even the combination of any two is possible in some parameter space. We have achieved the efficiency of the engine is greater than Carnot limit. The coefficient of performance of refrigerator also achieves larger than Carnot limit.

cond-mat.stat-mech↗

arXiv2015

Anomalous Brownian Refrigerator

We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the particle cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

cond-mat.stat-mech↗

arXiv2014

Single Particle Stochastic Heat Engine

We have performed an extensive analysis of a single particle stochastic heat engine constructed by manipulating a Brownian particle in a time dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems we observe that the operational characteristics are model dependent. Our results clearly rules out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.

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↗

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

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↗