Non-equilibrium Thermodynamics from First Principles

In this talk we present a fundamental first principles approach to understand non-equilibrium phenomena and the onset of complexity in nature. We begin by putting forward a simple observation, the analogous of the Principle of Equivalence in mechanics to its counterpart in (non-equilibrium) thermodynamics. We introduce our formulation 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. We thus put forward a generalized expression for the First Law of Thermodynamics, which has a virial-like expansion of the state variables and their higher-order spatial and temporal derivatives. Moreover, this generalized First Law hints at the presence of pairs of conjugate constants, that correspond to characteristic time and length scales for physical systems at various orders of complexity.