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We discuss spatio-temporal pattern formation in two separate thermal convective systems. In the first system, hydrothermal waves (HTW) are modeled numerically in an annular channel. A temperature difference is imposed across the channel, which induces a surface tension gradient on the free surface of the fluid, leading to a surface flow towards the cold side. The flow pattern is axially symmetric along the temperature gradient with an internal circulation for a small temperature difference. This axially symmetric flow (ASF) becomes unstable beyond a given temperature difference threshold, and subsequently, symmetry-breaking flow, i.e., rotational oscillating waves or HTW, appears. For the second system, Rayleigh-B\'enard convection (RBC) is experimentally studied in the non-turbulent regime. When a thin film of liquid is heated, the competing forces of viscosity and buoyancy give rise to convective instabilities. This convective instability creates a spatio-temporal non-uniform temperature distribution on the surface of the fluid film. The surface temperature statistics are studied in both these systems as `order' and `disorder' phase separates. Although the mechanisms that give rise to convective instabilities are different in both cases, we find an agreement on the macroscopic nature of the thermal distributions in these emergent structures., Comment: Submitted to the Journal of Non-equilibrium Thermodynamics

An approach that extends equilibrium thermodynamics principles to out-of-equilibrium systems is based on the local equilibrium hypothesis. However, the validity of the a priori assumption of local equilibrium has been questioned due to the lack of sufficient experimental evidence. In this paper, we present experimental results obtained from a pure thermodynamic study of the non-turbulent Rayleigh-B\'enard convection at steady-state to verify the validity of the local equilibrium hypothesis. A non-turbulent Rayleigh-B\'enard convection at steady-state is an excellent `model thermodynamic system' in which local measurements do not convey the complete picture about the spatial heterogeneity present in the macroscopic thermodynamic landscape. Indeed, the onset of convection leads to the emergence of spatially stable hot and cold domains. Our results indicate that these domains while break spatial symmetry macroscopically, preserves it locally that exhibit room temperature equilibrium-like statistics. Furthermore, the role of the emergent heat flux is investigated and a linear relationship is observed between the heat flux and the external driving force following the onset of thermal convection. Finally, theoretical and conceptual implications of these results are discussed which opens up new avenues in the study non-equilibrium steady-states, especially in complex, soft, and active-matter systems., Comment: Accepted in Physica A

In the paper, "Time & clocks: A thermodynamic approach" Lucia and Grisolia describe the connections between the physical nature of time and macroscopic irreversibility in thermodynamics. They also discuss the possibility of constructing a thermodynamic clock that links the two, through an approach based on the behaviour of a black body. Their work primarily focuses on the macroscopic irreversibilty, and their attempt to define 'thermodynamic time' is grounded on the concepts from non-equilibrium thermodynamics such as, entropy generation and time-dependent thermodynamic fluxes - in and out of the system. In this letter, we present a first principles approach based on the Maupertuis principle to describe the connection between time and thermodynamics for equilibrium phenomena. Our novel interpretation of the temperature as a functional allows us to extend our formalism to irreversible processes when the local equilibrium hypothesis is satisfied. Through our framework we also establish a functional relationship between equilibrium and non-equilibrium time-scales while distinguishing between the two.

In this paper, experimental data is presented and a simple model is developed for the time evolution of a F-amp \textit{E. Coli} culture population. In general, the bacteria life cycle as revealed by monitoring a culture's population consists of the lag phase, the growth (or exponential) phase, the log (or stationary) phase, and finally the death phase. As the name suggests, in the stationary phase, the population of the bacteria ceases to grow exponentially and reaches a plateau before beginning the death phase. High temporal resolution experimental observations using a unique light-scattering technique in this work reveal all the expected phases in detail as well as an oscillatory population behavior in the stationary phase. This unambiguous oscillation behavior has been suggested previously using traditional surveys of aliquots from a given population culture. An attempt is made to model these experimental results by developing a differential equation that accounts for the spatial distribution of the individual cells and the presence of the self-organizing forces of competition and dispersion. The main phases are well represented, and the oscillating behavior is attributed to intra-species mixing. It is also observed, that the convective motion arising out of intra-species mixing while plays a key role in limiting population growth, scales as $t^{-\alpha}$, where $\alpha$ is bounded by model parameters.

Soft-matter systems when driven out-of-equilibrium often give rise to structures that usually lie in-between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh-B\'enard convection system which when driven out-of-equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out-of-equilibrium., Comment: Submitted to Entropy

In this paper we present a detailed description of the statistical and computational techniques that were employed to study a driven far-from-equilibrium steady-state Rayleigh-B{\'e}nard system in the non-turbulent regime ($Ra\leq 3500$). In our previous work on the Rayleigh-B{\'e}nard convection system we try to answer two key open problems that are of great interest in contemporary physics: (i) how does an out-of-equilibrium steady-state differ from an equilibrium state and (ii) how do we explain the spontaneous emergence of stable structures and simultaneously interpret the physical notion of temperature when out-of-equilibrium. We believe that this paper will offer a useful repository of the technical details for a first principles study of similar kind. In addition, we are also hopeful that our work will spur considerable interest in the community which will lead to the development of more sophisticated and novel techniques to study far-from-equilibrium behavior., Comment: Submitted to Physica A

A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-B{\'e}nard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system's temperature manifold., Comment: To appear in Scientific Reports

Far-from-equilibrium systems are ubiquitous in nature. They are also rich in terms of diversity and complexity. Therefore, it is an intellectual challenge to be able to understand the physics of far-from-equilibrium phenomena. In this paper we revisit a standard tabletop experiment, the Rayleigh-B{\'e}nard convection, to explore some fundamental questions and present a new perspective from a first-principles point of view. How non-equilibrium fluctuations differ from equilibrium fluctuations, how emergence of order out-of-equilibrium breaks symmetries in the system, or how free-energy of a system gets locally bifurcated to operate a Carnot-like engine to maintain order? The exploration and investigation of these non-trivial questions are the focus of this paper., Comment: To appear in MRS Bulletin SI Bio-inspired "Far From Equilibrium" Materials, February 2019

The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the formation of molecules from atoms, of organisms, and of the society. In this sequence, order appears inside complex systems and randomness (entropy) is expelled to their surroundings. Key features of self-organizing systems are that they are open and they are far away from equilibrium, with increasing energy flowing through them. This work searches for global measures of such self-organizing systems, that are predictable and do not depend on the substrate of the system studied. Our results will help to understand the existence of complex systems and mechanisms of self-organization. In part we also provide insights, in this work, about the underlying physical essence of the Moore's law and the multiple logistic growth observed in technological progress., Comment: Complexity, 2016 (http://downloads.hindawi.com/journals/complexity/aip/8170632.pdf)

In recent times, the domain of network science has become extremely useful in understanding the underlying structure of various real-world networks and to answer non-trivial questions regarding them. In this study, we rigourously analyze the statistical properties of the bus networks of six major Indian cities as graphs in L- and P-space, using tools from network science. Although public transport networks, such as airline and railway networks have been extensively studied, a comprehensive study on the structure and growth of bus networks is lacking. In India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze their topological structure, and answer some of the basic questions on their evolution, growth, robustness and resiliency. We start from an empirical analysis of these networks, and determine their principle characteristics in terms of the complex network theory. The common features of small-world property and heavy tails in degree-distribution plots are observed in all the networks studied. Our analysis further reveals a wide spectrum of network topologies arising due to an interplay between preferential and random attachment of nodes. Unlike real-world networks, like the Internet, WWW and airline, which are virtual, bus networks are physically constrained in two-dimensional space by the underlying road networks. In order to understand the role of constraints in the evolution of these networks, we calculate their fractal dimensions that reveal a three-dimensional space-like evolution in a constrained two-dimensional plane. We also extend our study to understand the complex dynamical processes of epidemic outbreaks and information diffusion in these networks using SI and SIR models.

Bus transportation is considered as one of the most convenient and cheapest modes of public transportation in Indian cities. Due to their cost-effectiveness and wide reachability, they help a significant portion of the human population in cities to reach their destinations every day. Although from a transportation point of view they have numerous advantages over other modes of public transportation, they also pose a serious threat of contagious diseases spreading throughout the city. The presence of numerous local spatial constraints makes the process and extent of epidemic spreading extremely difficult to predict. Also, majority of the studies have focused on the contagion processes on scale-free network topologies whereas, spatially-constrained real-world networks such as, bus networks exhibit a wide-spectrum of network topology. Therefore, we aim in this study to understand this complex dynamical process of epidemic outbreak and information diffusion on the bus networks for six different Indian cities using SI and SIR models. This will allow us to identify epidemic thresholds for these networks which will help us in controlling outbreaks by developing node-based immunization techniques., Comment: Dynamical Systems: Theory and Application 2015, Poland

Through the past decade the field of network science has established itself as a common ground for the cross-fertilization of exciting inter-disciplinary studies which has motivated researchers to model almost every physical system as an interacting network consisting of nodes and links. Although public transport networks such as airline and railway networks have been extensively studied, the status of bus networks still remains in obscurity. In developing countries like India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer some of the basic questions on its evolution, growth, robustness and resiliency. In this paper, we model the bus networks of major Indian cities as graphs in \textit{L}-space, and evaluate their various statistical properties using concepts from network science. Our analysis reveals a wide spectrum of network topology with the common underlying feature of small-world property. We observe that the networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, like Internet, WWW and airline, which are virtual, bus networks are physically constrained. The presence of various geographical and economic constraints allow these networks to evolve over time. Our findings therefore, throw light on the evolution of such geographically and socio-economically constrained networks which will help us in designing more efficient networks in the future., Comment: Submitted to PLOS ONE

Murphy's Law is $not$ a law in the formal sense yet popular science often compares it with the Second Law of Thermodynamics as both the statements point toward a more disorganized state with time. In this paper, we first construct a mathematically equivalent statement for Murphy's Law and then disprove it using the intuitive idea that energy differences will level off along the paths of steepest descent, or along trajectories of least action., Comment: Complexity 2015

In this paper, we study the structural properties of the complex bus network of Chennai. We formulate this extensive network structure by identifying each bus stop as a node, and a bus which stops at any two adjacent bus stops as an edge connecting the nodes. Rigorous statistical analysis of this data shows that the Chennai bus network displays small-world properties and a scale-free degree distribution with the power-law exponent, $\gamma > 3$., Comment: International Conference on Complex Systems and Applications ICCSA 2014, France. https://halshs.archives-ouvertes.fr/halshs-01060875/document

A natural process is defined as an act, by which a system organizes itself with time. Any natural process drives a system to a state of greater organization. Organization is a progressive change, while evolution is expressed in the effects of accumulating marks acquired from contingent encounters. Co-existence of the system in states of maximum organization as well as maximum action forms the core idea of the paper. Major influences have been drawn from the Principle of Least Action. This allows us to see how this most basic law of physics determines the development of the system towards states with less action i.e. organized states. Based on this, it has been proposed, that the development of a system towards states of greater organization is cyclic in nature and thus evolution is a cyclic process., Comment: 11 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1004.3518 by other authors

The Principle of Least Action has evolved and established itself as the most basic law of physics. This allows us to see how this fundamental law of nature determines the development of the system towards states with less action, i.e., organized states. A system undergoing a natural process is formulated as a game that tends to organize the system in the least possible time. Also, other concepts of game theory are related to their profound physical counterparts. Although no fundamentally new findings are provided, it is quite interesting to see certain important properties of a complex system and their far-reaching consequences., Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:1004.3518 by other authors