Thermodynamics of fluctuations based on time-and-space averages

Abstract

We develop non-equilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in non-ergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider non-stationary processes, applying time-and-space averages to characterize non-ergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales but not at large length scales. We then characterize fluctuations in capillary-dominated systems, which are non-stationary due to the irreversibility of cooperative events.

References in corpus (22)

• Invariant Variation Problems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
• Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior
• Universal geometric constraints during epithelial jamming
• Experimental study of mutual information in a Maxwell Demon
• Broken detailed balance and non-equilibrium dynamics in living systems
• Coalescence of bubbles and drops in an outer fluid
• Viscous to Inertial Crossover in Liquid Drop Coalescence
• Spatial Fluctuations Of Fluid Velocities In Flow Through A Three-Dimensional Porous Medium
• The inexorable resistance of inertia determines the initial regime of drop coalescence
• Information-Theoretic Limits of Control
• Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
• Signatures of fluid-fluid displacement in porous media: wettability, patterns, and pressures
• Coalescence in low-viscosity liquids
• Fluctuating motion in an active environment
• Uncertainty relations and fluctuation theorems for Bayes nets
• Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation
• A no-go theorem for ergodicity and an Einstein relation
• Maxwell's demons with finite size and response time
• Predictive Maxwell's Demons