20.1 Non-equilibrium thermodynamics

Non-equilibrium thermodynamics tackles systems with gradients in temperature, pressure, or concentration. It's crucial for understanding transport phenomena, chemical reactions, and biological systems, extending classical thermodynamics to more complex scenarios.

Entropy production is key in non-equilibrium processes, measuring irreversibility and energy dissipation. The second law states that entropy always increases in isolated systems, highlighting the irreversible nature of these processes and their connection to gradients and fluxes.

Introduction to Non-Equilibrium Thermodynamics

Non-equilibrium thermodynamics fundamentals

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• Branch of thermodynamics dealing with systems not in thermodynamic equilibrium extends classical thermodynamics principles to systems with gradients in temperature, pressure, concentration, or other thermodynamic variables
• Applies to transport phenomena including heat transfer, mass transfer, and fluid dynamics, chemical reactions and combustion processes, biological systems and biophysics, materials science and engineering involving phase transformations, diffusion, and interfacial phenomena

Entropy production in non-equilibrium processes

• Measures irreversibility of a process and rate of entropy generation within a system quantifies dissipation of energy and generation of disorder in non-equilibrium processes
• Second law of thermodynamics states total entropy of an isolated system always increases over time in non-equilibrium processes, entropy production is always positive, indicating irreversible nature of these processes
• Related to gradients of thermodynamic variables (temperature, pressure, concentration) and fluxes of energy, mass, or other quantities rate of entropy production given by product of flux and corresponding thermodynamic force (gradient)

Advanced Concepts in Non-Equilibrium Thermodynamics

Systems far from equilibrium

• Linear non-equilibrium thermodynamics assumes system is close to equilibrium, fluxes linearly related to thermodynamic forces allows use of linear phenomenological equations (Fourier's law for heat conduction, Fick's law for diffusion)
• Far-from-equilibrium systems exhibit nonlinear behavior, linear approximations may no longer be valid more advanced theories required (extended irreversible thermodynamics, rational thermodynamics)
• Stability analysis important in studying far-from-equilibrium systems concepts of dissipative structures, self-organization, and pattern formation can emerge in systems driven far from equilibrium (Rayleigh-Bénard convection cells, Belousov-Zhabotinsky reaction, Turing patterns)

Onsager reciprocal relations

• Developed by Lars Onsager, describe coupling between different transport processes in a system near equilibrium
• Relations state matrix of phenomenological coefficients ($L_{ij}$), relating fluxes ($J_i$) to thermodynamic forces ($X_j$), is symmetric: $L_{ij} = L_{ji}$
• Symmetry implies gradient in one thermodynamic variable can induce flux of another variable, and vice versa (temperature gradient inducing mass flux (Soret effect), concentration gradient inducing heat flux (Dufour effect))
• Important consequences for efficiency of coupled transport processes and design of thermodynamic devices (thermoelectric generators, fuel cells)