20.1 Non-equilibrium thermodynamics
2 min read•july 23, 2024
tackles systems with gradients in temperature, pressure, or concentration. It's crucial for understanding , , and , extending classical thermodynamics to more complex scenarios.
is key in non-equilibrium processes, measuring and energy . The second law states that entropy always increases in isolated systems, highlighting the irreversible nature of these processes and their connection to gradients and .
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 , , 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
- 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
- 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 , linear approximations may no longer be valid more advanced theories required (, )
- important in studying far-from-equilibrium systems concepts of , , and can emerge in systems driven far from equilibrium (, , )
Onsager reciprocal relations
- Developed by Lars Onsager, describe coupling between different transport processes in a system near equilibrium
- Relations state matrix of (), relating fluxes () to thermodynamic forces (), is symmetric:
- Symmetry implies gradient in one thermodynamic variable can induce flux of another variable, and vice versa (temperature gradient inducing mass flux (), concentration gradient inducing heat flux ())
- Important consequences for efficiency of coupled transport processes and design of thermodynamic devices (thermoelectric generators, fuel cells)
Key Terms to Review (27)
Belousov-Zhabotinsky Reaction: The Belousov-Zhabotinsky reaction is a classic example of a non-equilibrium chemical reaction that exhibits oscillatory behavior, where the concentration of reactants and products varies periodically over time. This reaction showcases how chemical systems can display complex dynamics and self-organization, which are fundamental concepts in non-equilibrium thermodynamics.
Biological systems: Biological systems refer to complex networks of biological entities that interact to maintain life and promote various physiological functions. These systems operate through various processes including metabolism, growth, reproduction, and response to stimuli, all of which are essential for the survival of organisms. Understanding these systems is crucial in the context of how they maintain homeostasis and respond to changes in their environment.
Chemical Reactions: Chemical reactions are processes that involve the transformation of reactants into products through the breaking and forming of chemical bonds. These reactions are essential in understanding energy changes, especially in relation to entropy, as they can lead to variations in disorder and influence the direction and spontaneity of a process.
Convection: Convection is the process of heat transfer through the movement of fluids, where warmer, less dense regions of the fluid rise while cooler, denser regions sink. This continuous movement creates a cycle that transfers heat, playing a crucial role in various physical systems, from atmospheric phenomena to heating in buildings. Understanding convection helps to explain how energy is distributed in fluids and its impact on temperature variations.
Diffusion: Diffusion is the process by which particles spread from areas of high concentration to areas of low concentration due to random motion. This phenomenon is a fundamental concept in understanding how substances interact in various systems, impacting energy distribution and equilibrium. The movement of molecules during diffusion occurs until a uniform concentration is achieved, playing a crucial role in gas behavior and non-equilibrium processes.
Dissipation: Dissipation refers to the process in which energy is dispersed or transformed into a less useful form, typically as heat, leading to a decrease in the availability of energy for doing work. This phenomenon is central to understanding non-equilibrium thermodynamics, where systems are not in a state of balance and energy flows occur, resulting in entropy generation. The dissipation of energy is crucial for explaining the behavior of systems that are far from equilibrium and the inevitable tendency towards disorder.
Dissipative structures: Dissipative structures are ordered systems that arise in non-equilibrium thermodynamics, where a steady flow of energy or matter maintains their organization despite the tendency towards disorder. These structures demonstrate how systems can self-organize and maintain stability while dissipating energy, highlighting the intricate relationship between entropy and order in complex systems.
Dufour Effect: The Dufour effect describes the phenomenon where a temperature gradient within a material leads to a concentration gradient of species within that material. This effect is important in non-equilibrium thermodynamics as it illustrates how energy transport can influence mass transport, highlighting the interplay between thermal and concentration gradients in systems that are not in equilibrium.
Entropy production: Entropy production refers to the generation of entropy in a system as it moves away from equilibrium due to irreversible processes. This concept is crucial in understanding non-equilibrium thermodynamics, as it quantifies the degree of disorder and energy dispersal within a system when external constraints drive changes. In essence, entropy production indicates how far a system is from equilibrium and helps to explain the direction of natural processes.
Extended irreversible thermodynamics: Extended irreversible thermodynamics is a theoretical framework that extends classical irreversible thermodynamics by incorporating additional physical phenomena such as non-equilibrium states and finite-size effects. This approach allows for a more accurate description of systems far from equilibrium, accounting for the complex interactions and behaviors that arise in such conditions. It emphasizes the role of gradients in thermodynamic variables and introduces new constitutive relations that help describe the dynamics of systems undergoing irreversible processes.
Fluxes: Fluxes refer to the rates at which a quantity, such as mass, energy, or momentum, passes through a specified surface per unit time. In non-equilibrium thermodynamics, fluxes are crucial for understanding how systems evolve over time as they move away from equilibrium, highlighting the flow of energy and matter in processes like heat conduction and diffusion.
Irreversibility: Irreversibility refers to the natural tendency of processes to move towards a state of increased disorder, meaning they cannot spontaneously revert to their original state without external work or intervention. This concept is central to understanding the directionality of thermodynamic processes and plays a crucial role in concepts like entropy and the second law of thermodynamics, as well as in analyzing both equilibrium and non-equilibrium states.
Linear non-equilibrium thermodynamics: Linear non-equilibrium thermodynamics is a framework that describes the behavior of systems that are not in thermodynamic equilibrium, focusing on small deviations from equilibrium conditions. This approach allows for the analysis of transport processes, such as heat conduction and diffusion, under the assumption that these processes are linear with respect to the driving forces acting on the system. By applying linear relationships, it simplifies the complex dynamics involved in non-equilibrium phenomena.
Non-equilibrium thermodynamics: Non-equilibrium thermodynamics is the branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium, where gradients in temperature, pressure, or chemical potential drive the system towards a state of balance. This field studies how these gradients lead to irreversible processes and how energy and matter are exchanged within systems as they evolve over time.
Nonlinear behavior: Nonlinear behavior refers to systems where the output is not directly proportional to the input, meaning small changes in one variable can cause large changes in another. This kind of behavior is common in complex systems, particularly those that are out of equilibrium, where relationships between variables can become highly sensitive and unpredictable, leading to phenomena such as chaos and bifurcations.
Onsager's Reciprocal Relations: Onsager's reciprocal relations are a set of principles in non-equilibrium thermodynamics that establish a relationship between different thermodynamic fluxes and their corresponding forces. These relations demonstrate that for systems near equilibrium, the transport coefficients are symmetric, meaning that the effect of one driving force on a flux is equal to the effect of the corresponding flux on the same driving force in reverse.
Pattern formation: Pattern formation refers to the process by which ordered structures emerge in a system far from equilibrium, driven by various physical, chemical, or biological interactions. This phenomenon is significant because it illustrates how complex patterns can arise from simple rules and interactions, revealing the underlying mechanisms of self-organization in non-equilibrium thermodynamics.
Phase transformations: Phase transformations refer to the process in which a substance changes from one state of matter to another, such as solid, liquid, or gas. This concept is crucial in understanding how materials behave under varying temperature and pressure conditions, as well as the energy exchanges that accompany these changes.
Phenomenological Coefficients: Phenomenological coefficients are parameters that characterize the relationship between thermodynamic fluxes and their driving forces in non-equilibrium thermodynamics. They serve as crucial metrics for understanding how various transport processes, such as heat conduction and diffusion, respond to gradients in temperature, concentration, or other state variables. These coefficients are integral in formulating constitutive equations that describe the behavior of materials under non-equilibrium conditions.
Rational thermodynamics: Rational thermodynamics is an approach to the study of thermodynamic systems that emphasizes the use of mathematical modeling and systematic reasoning to analyze non-equilibrium phenomena. This framework combines classical thermodynamic principles with modern mathematical techniques, allowing for a more comprehensive understanding of irreversible processes and complex systems. By focusing on the state variables and their relationships, rational thermodynamics facilitates the description and prediction of how systems evolve away from equilibrium.
Rayleigh-Bénard convection cells: Rayleigh-Bénard convection cells are fluid motion patterns that occur when a fluid layer is heated from below and cooled from above, resulting in the formation of distinct cells or patterns of circulation. This phenomenon illustrates the transition from conduction to convection and is a key example of non-equilibrium thermodynamics, demonstrating how temperature gradients can induce flow in fluids.
Second law of thermodynamics: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and it dictates the direction of thermodynamic processes. This principle establishes that energy transformations are not 100% efficient, highlighting the inherent tendency for systems to move towards a state of greater disorder or randomness, affecting heat transfer, the performance of engines, and various processes in nature.
Self-organization: Self-organization is the process by which a system spontaneously arranges itself into a structured or patterned state without external guidance or control. This phenomenon is crucial in understanding how complex structures and patterns emerge from simple interactions within non-equilibrium systems, highlighting the ability of systems to evolve and adapt over time.
Soret effect: The Soret effect, also known as thermodiffusion, is the phenomenon where a temperature gradient causes the separation of components in a mixture, leading to concentration gradients. This effect plays a crucial role in understanding how substances behave under non-equilibrium conditions, as it demonstrates how temperature influences the distribution of particles in a mixture, which can affect transport properties and phase behavior.
Stability analysis: Stability analysis is a method used to determine the stability of a system or its equilibrium states by assessing how small perturbations affect its behavior. It often involves evaluating the response of a system to changes in parameters, helping to predict whether it will return to equilibrium or diverge away from it. This concept is crucial in understanding phase transitions and non-equilibrium processes, as it provides insight into how systems behave under varying conditions.
Transport phenomena: Transport phenomena refers to the study of the transfer of mass, energy, and momentum in physical systems. This concept is crucial in understanding how these transfers occur in non-equilibrium conditions, where systems are not in a state of balance. It provides insights into how substances move and interact, which is essential for analyzing processes like diffusion, heat conduction, and fluid flow.
Turing patterns: Turing patterns refer to the spatial arrangements or structures that emerge in a system due to the interplay of reaction-diffusion processes, as proposed by mathematician Alan Turing. These patterns arise in non-equilibrium conditions when chemical substances interact and diffuse at different rates, leading to self-organization and the formation of distinct patterns such as stripes or spots, which are prevalent in nature, such as in animal coats and biological systems.