An enhanced theory for nonlinear and irreversible thermodynamics

Classic thermodynamics universally describes unique and reversible systems in equilibrium integrating state variables and state functions, such as entropy and free energy. But many situations (e.g. biology shaped by evolution) are neither unique or reversible – they are nonlinear with a multiplicity of outcomes. Nobel laureate Ilya Prigogine seminally theorized irreversible and nonlinear thermodynamics, but he restricted his theorizing to a macroscopic description where microscopic effects are not accounted. Two theorists from the Center for Nonlinear Phenomenon and Complex Systems in Belgium expanded Prigogine’s theory to incorporate a thermodynamic microscopic-macroscopic interaction. They report on their work in Chaos: An Interdisciplinary Journal of Nonlinear Science.

Authors Grégoire Nicolis and Yannick De Decker started with Prigogine’s Ansatz where entropy is locally expressed in terms of state variables, from which entropy production, representing the dissipation of a system, can be obtained. They added terms for microscopic processes that appear as fluctuations undergoing stochastic processes without memory. They thereby deduce a fluctuating entropy production that can take a negative value, but only locally, the system’s sum total remains positive. In these situations, “instead of a system dissipating work on its environment, it uses its environment to produce work,” Nicolis explains.

The paper also offers a linear description in terms of probability distributions for the thermodynamic states of the nonlinear, irreversible system. Irreversibility is here linked to the asymmetry of forward and backward transitions with respect to time reversal.

Nicolis hopes to build on this work to account for memory effects and for the deterministic character of the underlying microscopic dynamics. Additionally, future irreversible thermodynamic theory could establish links with complexity and information theories, which also pertain to emergent properties, critical for multiple outcome systems.

Source: “Stochastic approach to irreversible thermodynamics,” by Grégoire Nicolis and Yannick De Decker, Chaos: An Interdisciplinary Journal of Nonlinear Science (2017). The article can be accessed at https://doi.org/10.1063/1.5001303 .