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Non-equilibrium thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Unlike classical thermodynamics, which generally assumes that the systems being studied are in equilibrium or close to equilibrium, non-equilibrium thermodynamics applies to more general situations, taking into account the flow of matter and energy over time.
Introduction
In classical thermodynamics, systems are typically studied when they are in equilibrium. At equilibrium, the macroscopic properties of a system do not change over time. However, many real-world processes are far from equilibrium, such as chemical reactions, biological processes, and heat transfer. Non-equilibrium thermodynamics provides tools and concepts to study such processes.
Basic concepts of discontinuous thermodynamics
Balance vs. unbalance
A common way to understand equilibrium is to consider a cup of hot coffee left in a room. In the beginning, the coffee is at a higher temperature than the surrounding air, and over time, it loses heat until it reaches the same temperature as the room. When the temperatures equalize and there is no further net exchange of heat, the system is said to be in equilibrium.
In contrast, non-equilibrium conditions can be observed when coffee is constantly stirred or when heat is applied to it. These are dynamic situations where macroscopic properties are constantly changing.
Irreversible processes
Non-equilibrium thermodynamics is often concerned with irreversible processes. These are processes that cannot reverse on their own. For example, heat flows from a hot object to a cold object without any external work; this process is irreversible because the reverse does not occur naturally. To make heat flow from a cold object to a hot object we need external work (e.g. a refrigerator).
Thermodynamic forces and fluxes
An essential concept in non-equilibrium thermodynamics is the relationship between thermodynamic forces and flows. Thermodynamic forces are gradients, such as temperature gradients, concentration gradients, or chemical potential gradients, that drive changes in a system. Flows represent the flow of quantities such as heat or matter in response to these forces.
J = L * X
Here, J
is the flux, X
is the thermodynamic force, and L
is the incidence coefficient, a proportionality constant that describes the response of the system.
Linear non-equilibrium thermodynamics
Linear non-equilibrium thermodynamics is a field that focuses on systems where forces and flows are linearly related, which is a useful approximation near equilibrium. In linear systems, the principle of superposition applies, making the mathematical analysis more manageable.
Applications in physical chemistry
Chemical reactions
Consider a simple chemical reaction where reactants A and B combine to form product C:
A + B → C
In a non-equilibrium state, the concentrations of A, B, and C change over time. The rates of these changes can be described by reaction kinetics. Non-equilibrium thermodynamics gives information about how changes in external conditions, such as temperature or pressure, affect the reaction rate and direction.
Spread
An everyday example of diffusion as a non-equilibrium process is the spreading of ink in water. Initially localized, the ink molecules move randomly due to thermal motion, leading to diffusion. This process is driven by the concentration gradient and can be studied using Fick's laws of diffusion.
In the above illustration, ink spreads in water, illustrating diffusion driven by a concentration gradient.
Convection
Convection is the bulk motion of groups of molecules within fluids (gases and liquids) and is another non-equilibrium process. It is essential in situations where heat needs to be transferred in the fluid, such as in boiling water. Here, convection currents are set up, which transfer heat efficiently away from the heat source.
This visual illustration shows a convection cell, where heat causes fluid to move in a circular pattern, allowing for efficient heat transfer.
Entropy production
In non-equilibrium systems, entropy production is constant, which is in contrast to equilibrium systems where entropy is maximum and production stops. The second law of thermodynamics asserts that entropy in an isolated system has a tendency to increase, which is consistent with many non-equilibrium processes.
Consider the melting of ice in open air; when this happens, there is no net exchange of heat with the surroundings, the entropy of the water (system) and the air (surroundings) increases, indicating irreversible processes driven by gradients.
Prigogine's theorem
Ilya Prigogine furthered the understanding of non-equilibrium systems through his theorem on minimum entropy production, which states that for linear systems close to equilibrium, the entropy production rate is minimal. This principle helps in understanding and predicting the direction of processes in non-equilibrium thermodynamics.
Biological systems and non-equilibrium thermodynamics
Living systems are prime examples of non-equilibrium thermodynamic systems. They are open systems that exchange matter and energy with their environment, allowing for evolution and maintenance far from equilibrium.
Metabolism
The metabolic pathway consists of a series of biochemical reactions that take place within the cell, requiring a constant input of energy and mass. The energy currency ATP is produced and consumed, which drives these processes and maintains a state far from equilibrium.
Homeostasis
Homeostasis is a biological principle whereby living systems maintain stable internal conditions despite external changes. This regulation ensures that variables such as temperature, pH and ion concentrations are controlled, demonstrating key non-equilibrium thermodynamics in action.
Non-equilibrium thermodynamics can be used to analyze these highly regulated and energy-expensive processes, and to model how effectively organisms cope with environmental variations.
Conclusion
Non-equilibrium thermodynamics broadens the scope of traditional thermodynamics by taking into account the dynamic nature of real-world processes. By understanding and applying the principles of non-equilibrium thermodynamics, scientists can better describe and predict the behavior of a wide variety of systems, from simple physical systems to complex biological organisms.