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# Non-equilibrium thermodynamics from First Principles

# Non-equilibrium thermodynamics from First Principles

## Abstract:

In this talk I present a fundamental first principles approach to undestand non-equilibrium phenomena and the onset of complexity in nature. I begin the talk by putting forward a simple observation, the analogous of the Principle of Equivalence in Thermodynamics. I probe this by laying out an equivalent field-theoretic approach to classical thermodynamics. The central core of this idea is to identify a thermodynamically open system as a scalar field over a symplectic energy manifold. Once the Lagrangian density is defined in terms of thermodynamic state variables, the Euler-Lagrange equations yield the steady-state energy conservation law. The salient feature of this formulation is the emergence of the spatial and temporal derivatives of these state variables as non-equilibrium corrections to the First Law of Thermodynamics. I thus put forward a generalized First Law equation, whcih has a virial-like expansion of the state variables and their higher-order spatial and temporal derivatives. Moreover, the generalized First Law hints at the presence of a pair of constants, that corresponds to characteristic time and length scales for physical systems at various orders of complexity.