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-Bénard system in the non-turbulent regime (Ra ≤ 3500). In our previous work on the Rayleigh-Bénard 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. arXiv:1905.08761v1 [cond-mat.soft]

Complexity in nature is astounding yet the explanation lies in the fundamental laws of physics. The Second Law of Thermodynamics and the Principle of Least Action are the two theories of science that have always stood the test of time. In this article, we use these fundamental principles as tools to understand how and why things happen. In order to achieve that, it is of absolute necessity to define things precisely yet preserving their applicability in a broader sense. We try to develop precise, mathematically rigorous definitions of the commonly used terms in this context, such as action, organization, system, process, etc., and in parallel argue the behavior of the system from the first principles. This article, thus, acts as a mathematical framework for more discipline‐specific theories. © 2015 Wiley Periodicals, Inc. Complexity 21: 307–317, 2016

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 selforganization. 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.

In this paper, we model the bus networks of six major Indian cities as graphs in L-space, and evaluate their various statistical properties. While 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 transport plays an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer basic questions on its evolution, growth, robustness and resiliency. Although the common feature of small-world property is observed, our analysis reveals a wide spectrum of network topologies arising due to significant variation in the degree-distribution patterns in the networks. We also observe that these networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, such as Internet, WWW and airline, that are virtual, bus networks are physically constrained. Our findings therefore, throw light on the evolution of such geographically and constrained networks that will help us in designing more efficient bus networks in the future.

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-Bénard 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.