Thermodynamics of action and organization in a system

Abstract

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 Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis

“…For example, the path taken by a ball rolling down a frictionless ramp can be calculated using Newton's Laws of motion (a 'bottom-up' approach), or using Lagrangian mechanics (Hamilton's principle) simply by requiring that the ball reach the bottom by spending the least total amount of energy (a 'top-down' approach) [113]. These principles have begun to be applied to understanding biological complexity, collective behaviour, evolution and brain function [114][115][116][117][118].…”

An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

“…The same system when driven out of equilibrium gives rise to flows that force the system to relax back into its equilibrium state. The rate of relaxation is governed by how far the system has been driven out of equilibrium [ 1 , 2 , 3 ]. Soft-matter systems in this respect are especially fascinating as they often give rise to order as long as the driving field maintains it out of equilibrium [ 1 , 4 , 5 ].…”

An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-Bénard Convection

“…The same system when driven out-of-equilibrium gives rise to flows that forces the system to relax back into its equilibrium state. The rate of relaxation is governed by how far the system has been driven out-of-equilibrium [1][2][3]. Soft-matter systems in this respect are especially fascinating as they give often rise to order as long as the driving field maintains it out-of-equilibrium [1,4,5].…”