Studies on the Emergence of Order in Out-of-equilibrium Systems

Chatterjee, Atanu

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Studies on the Emergence of Order in Out-of-equilibrium Systems

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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. This work 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 as the temperature manifold bifurcates into regions of emergent order (sources) and disorder (sink). These localized domains which coexist together, reveal equilibrium-like fluctuations for the temperature scalar. We extend these experimental results to derive a thermodynamic equation of state for a driven system with emergent order from the first principles. We present a field theoretic formalism by defining the Lagrangian density as a function of a generic thermodynamic scalar. Our definition of the thermodynamic Lagrangian density involves two components, the internal work or the coherent part which gives rise to emergent order, and the internal dissipation or the incoherent part which acts as the internal sink. The salient feature of this formulation is that it takes into account the spatial and temporal gradients of the thermodynamic scalar as the system is driven out-of-equilibrium, similar to the Rayleigh-Bénard system. The action functional defined on this scalar manifold connects local equilibrium-like domains. On minimizing the action and solving the Euler-Lagrange equation, we obtain a generalized thermodynamic equation of state for a driven system with emergent order. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system's temperature manifold.

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