Stochastic Thermodynamics/Active particle Heat Engines:
In the last couple of decades Stochastic Thermodynamics has emerged as a very exciting field of research. This is a framework that connects Stochastic Dynamics at an individual trajectory level to Thermodynamics which is considered to be a macroscopic formulation. One application of stochastic thermodynamics is it's use in study of micro heat engines. Our group at IIT, Delhi works on heat engines motivated by recent microscopic experimental realizations of engines like Carnot or Stirling. We study their properties in terms of work, heat and efficiency and compare them with their thermodynamic counterparts. We also are studying active particle heat engines (consisting of self propelled particles e.g bacteria) in this regard.
Biophysics is a research area which looks at biologically motivated problems by using Physics tools. Biophysics deals with almost all biological scales, from single molecules to multiple cells. Excellent experimental techniques provide new insights. Theoretical models can be tested with experimental observations or vice-versa. Interdisciplinary nature motivates collaborations among many different fields. Bacterial motility has been a subject of fascination for a long time. There are numerous types of bacteria in the world of different shapes, sizes and hence they also show various types of motility e.g. using flagella, shape change, gliding etc. Some bacteria including human pathogen Neisseria gonorrhoeae perform a particular type of motion called as Twitching motility. These bacteria use so called type IV pili to propel themselves over surfaces. Pili are long polymeric structures given out of the bacterial body which adhere to the surface and then retract. Thus, pulling the cell body. Recent experiments performed on these bacteria suggest that several pili co-operate in bacterial motion and that their co-ordination may be based on a tug-of-war between pili pulling in different directions. I am interested in looking at Twitching motility in a theoretical point of view with a so called stochastic tug-of-war model which myself and my collaborators at Max Planck Institute of Colloids and Interfaces, Potsdam have developed. We also have strong collaborations with experimentalists at the University of Cologne. I would like to test the model with experimental observations. I would also like to test the generality of this model by using it to study other bacteria which perform Twitching motility.
Non-equilibrium statistical physics has been a frontier area in physics for a long time. Many systems such as magnetic, colloidal, biological or chemical are essentially non-equilibrium. Unlike equilibrium systems absence of any formal treatment opens up many opportunities to study simple but non-trivial models. Recent developments in this area namely fluctuation theorems, Jarzynski equality have changed the view of looking at non-equilibrium systems. Though well established, usefulness of these relations is still uncertain. I am interested in addressing this question in a more quantitative way by looking at model systems, and in connections to single molecule experiments.
Past research :
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of constitutive gene expression and compare such descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error of models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.
1) Sources of stochasticity in constitutive and autoregulated gene expression, Rahul Marathe, David Gomez, Stefan Klumpp,
Physica Scripta, in press (2012).
2) Deterministic and stochastic descriptions of gene expression dynamics, Rahul Marathe, Veronika Bierbaum, David Gomez, Stefan Klumpp,
J. Stat. Phys. in press (2012).
3) Sources of stochasticity in autoregulated gene expression, David Gomez, Rahul Marathe, Stefan Klumpp, under preparation.
In equilibrium physics, using the Gibbs theory of ensembles one can derive macroscopic physical properties of a system from its microscopic Hamiltonian. In non equilibrium physics there is no equivalent procedure for going from the microscopic to the coarse-grained picture. In fact we can define a non equilibrium system as one which cannot be described by any of the equilibrium ensembles. Examples of non equilibrium processes/systems are Brownian motion, heat and electrical particle transport, Granular materials and Glassy systems. The reasons that the equilibrium description breaks down in these systems can be various: for example there may be no Hamiltonian description; or the Hamiltonian is time-dependent; or relaxation times are extremely slow, etc.
In last decade very interesting relations namely Jarzynski equality and fluctuation theorems relating non equilibrium quantities to equilibrium one were proven. We studied a model system in this context of Jarzynski relation and fluctuation theorems. We studied the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. In this problem using Glauber dynamics we performed Monte-Carlo simulations to find the work distributions at different driving rates. We found that in general the work-distributions are broad
with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates were studied analytically. We verified that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.
1) Work distribution functions for hysteresis loops in a single-spin system, Rahul Marathe and Abhishek Dhar, Phys. Rev. E 72, 066112 (2005) .
The idea of constructing miniature versions of engines, motors and pumps has been an interesting one. The earliest theoretical construct of such a device is probably Feynman's pawl-and-ratchet model discussed in Feynman Lectures. In this article Feynman uses this simple microscopic model to demonstrate why a Maxwell's demon cannot work. Motivated by recent studies on models of particle and heat quantum pumps, we studied similar simple classical models and examined the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we studied do not have particle transport.
In the biological cells molecular motors like kinesins, dyneins etc. move on the micro tubules or actin filaments, it is very interesting as these molecules are in a very noisy environment and still they can move uni-directionally. Number of studies on exclusion process where particles hop from one site to other relate to the motion of these motors. Here there is a particle transport. We studied a similar particle pump model where the hopping rates at two given sites were time dependent. This could be a possible model for ion channels in cells. We studied the long time properties of this model by numerical simulations and a novel perturbative treatment. We have also extended above model from two site pump model to more general all site pump model. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.
1) Two simple models of classical heat pumps, Rahul Marathe, A. M. Jayannavar, and Abhishek Dhar, Phys. Rev. E 75, 030103(R) (2007).
2) Driving particle current through narrow channels using a classical pump, Kavita Jain, Rahul Marathe, Abhishek Chaudhuri, Abhishek Dhar,
Phys. Rev. Lett., 99, 190601 (2007).
3) Particle current in a symmetric exclusion process with time-dependent hopping rates, Rahul Marathe, Kavita Jain, Abhishek Dhar,
Second Law of Thermodynamics precludes cyclic extraction of energy from an isolated system. This impossibility is well established for macroscopic systems and also for small systems under very general conditions. However in this recent work, we discuss the possibility of extraction of energy from a single heat bath in a cyclic process, under some special initial conditions. We give an explicit example in which a system initially prepared in a microcanonical ensemble, is able to perform such operation. Our example consists of a single isolated particle and a quasi-static process involving nontrivial splits and collapses of orbits, and it is inspired by a celebrated sequel of the Maxwell demon: the Szilard engine. The microcanonical initial condition allows us to design a protocol where measurement is not necessary unlike original Szilard engine. We also discuss the limitations and possible extensions of this microcanonical engine.
1) Cooling Classical particles with a microcanonical Szilard engine, Rahul Marathe and J. M. R. Parrondo,
Phys. Rev. Lett. 104, 245704 (2010).
Mesoscopic systems of micron size have recently been studied extensively. In these systems, at low temperatures the mean free path of an electron can exceed the sample dimensions. Thus, maintaining the coherence of the single particle wave function across the entire sample. In such coherent systems several novel effects have been observed which are supposed to have ``no'' classical analogue. Motivated by these studies on current magnification in quantum mesoscopic systems we consider sound and heat transmission in classical models of oscillator chains. A loop of coupled oscillators is connected to two leads through which one can either transmit monochromatic waves or white noise signal from heat baths. We look for the possibility of current magnification in this system due to some asymmetry introduced between the two arms in the loop. We find that current magnification is indeed obtained for particular frequency ranges. However the integrated current shows the effect only in the presence of a pinning potential for the atoms in the leads. We also study the effect of anharmonicity on current magnification.
1) Energy current magnification in coupled oscillator loops, Rahul Marathe, Abhishek Dhar, Arun Jayannavar, Phys. Rev. E 82, 031117 (2010).
This article has also been selected for the September 20, 2010 issue of Virtual Journal of Nanoscale Science and Technology.