Punyabrata Pradhan

Approximate thermodynamic structure for driven lattice gases in contact.

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. For both attractive and repulsive nearest-neighbor interactions among particles and for a wide range of parameter values, we find that, to a good approximation, one could define an intensive thermodynamic variable, such as the equilibrium chemical potential, that determines the final steady state for two initially separated driven lattice gases brought into contact. However, due to nontrivial contact dynamics, there are also observable deviations from this simple thermodynamic law. To illustrate the role of the contact dynamics, we study a variant of the zero-range process and discuss how the deviations could be explained by a modified large-deviation principle. We identify an additional contribution to the large-deviation function, which we call the excess chemical potential, for the variant of the zero-range process as well as the driven lattice gases. The excess chemical potential depends on the specifics of the contact dynamics and is in general a priori unknown. A contact dependence implies that, even though an intensive variable may equalize, the zeroth law could still be violated.

Nonequilibrium fluctuation theorems in the presence of local heating.

We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of {exp(-betaW) to its theoretical mean value, where W is the work done on the test system and beta is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.

Gammalike mass distributions and mass fluctuations in conserved-mass transport processes.

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that the joint mass distribution of subsystems is factorized in the thermodynamic limit. The factorization condition is not too restrictive as it would hold in systems with short-ranged spatial correlations. To demonstrate the result, we revisit a broad class of mass transport models and its generic variants, and show that the variance of the subsystem mass in these models is proportional to the square of its mean. This particular functional form of the variance constrains the subsystem mass distribution to be a gamma distribution irrespective of the dynamical rules.

Cluster-factorized steady states in finite-range processes.

We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbors, with a rate that depends on the occupation of all the neighboring sites within a range R. This finite-range process (FRP) for R=0 reduces to the well-known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of a cluster-weight function of (R+1) occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.

Spatial correlations, additivity, and fluctuations in conserved-mass transport processes.

We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion, and coalescence of masses. We find that the spatial correlations are in general short-ranged and, consequently, on a large scale, these transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibrium-like additivity property and, consequently, a fluctuation-response relation, which help us to obtain subsystem mass distributions in the limit of subsystem size large.

Nonequilibrium fluctuation theorems in the presence of a time-reversal symmetry-breaking field and nonconservative forces

We study nonequilibrium fluctuation theorems for classical systems in the presence of a time-reversal symmetry-breaking field and nonconservative forces in a stochastic as well as a deterministic setup. We consider a system and a heat bath, called the combined system, and show that the fluctuation theorems are valid even when the heat bath goes out of equilibrium during driving. The only requirement for the validity is that, when the driving is switched off, the combined system relaxes to a state having a uniform probability measure on a constant energy surface, consistent with microcanonical ensemble of an isolated system.

Einstein relation and hydrodynamics of nonequilibrium mass transport processes

It is well recognized that the relative position of the center of mass (pCOM) with respect to the base of support (BOS) is a determining factor in the maintenance of balance. However, during gait the dynamic nature of the BOS is not well defined and in most studies is completely ignored. Prior work tends to focus on the variability in the position of the center of mass (COM) with respect to the laboratory reference frame to attempt to quantify dynamic balance. We propose a modified method whereby the position of the COM in an end-effector based coordinate system may be used as an improved estimate of threat to balance during gait. The distance (DN) of the projection of the COM (pCOM) from the reference axis, normalized by half the foot length for inter-subject comparison, is an estimate of the gravitational moment arm. It can be shown that in concordance with theory, balance impaired subjects with spastic cerebral palsy (CP) have a larger DN than their typically developing peers. Furthermore, when compared with variational methods, DN shows better discriminative ability in characterizing groups.

Additivity property and emergence of power laws in nonequilibrium steady states

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.

Interacting particles in a periodically moving potential: traveling wave and transport.

We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.

Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles.

Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation, a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.