Nonequilibrium Thermodynamics Simulations

Nonequilibrium Thermodynamics Simulations Visually

Explore Nonequilibrium Thermodynamics with interactive simulations. Understand entropy production, fluxes, forces, and the dynamics of systems far from equilibrium.

Entropy Production Fluxes & Forces Onsager Relations Linear Response Steady States Transport Processes

What is Nonequilibrium Thermodynamics?

Nonequilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Unlike classical thermodynamics, which focuses on equilibrium states, nonequilibrium thermodynamics studies the dynamics of systems with gradients in temperature, pressure, concentration, or other intensive properties.

The field provides a framework for understanding how systems evolve toward equilibrium and how they behave when maintained in nonequilibrium steady states by external constraints. Central to this field are concepts like entropy production, fluxes and forces, and the Onsager reciprocal relations.

Nonequilibrium thermodynamics has wide-ranging applications in biology, chemistry, materials science, and engineering, particularly in understanding transport processes, chemical reactions, and pattern formation in complex systems.

Entropy Production

Understanding irreversible processes and entropy generation

Entropy Information

Select a process type to see its entropy production characteristics.

Current Process:

Heat Conduction

Entropy Production Rate:

0.0 σ

Flux-Force Relationships

Linear and nonlinear relationships in nonequilibrium systems

Flux-Force Relationships

In nonequilibrium thermodynamics, fluxes (J) are driven by thermodynamic forces (X) through relationships of the form:

J = L × X

Where:
J = Flux (flow of matter, energy, etc.)
X = Thermodynamic Force (gradient)
L = Kinetic Coefficient (conductance)

Near vs Far From Equilibrium:

  • Near Equilibrium: Linear relationships with constant coefficients
  • Far From Equilibrium: Nonlinear relationships, possible instabilities
  • Coupled Processes: Multiple fluxes driven by multiple forces

Onsager Reciprocal Relations

Symmetry in coupled transport processes

Onsager Relations

For coupled processes near equilibrium:

J₁ = L₁₁X₁ + L₁₂X₂
J₂ = L₂₁X₁ + L₂₂X₂

Reciprocal Relation:
L₁₂ = L₂₁

Key Concepts:

  • Reciprocity: Cross-coefficients are equal
  • Microscopic Reversibility: Foundation of reciprocity
  • Time-Reversal Symmetry: Applies to microscopic laws

Example: Thermoelectric Effects

Seebeck and Peltier effects demonstrate Onsager reciprocity:

  • Voltage generates heat flow (Peltier)
  • Temperature gradient generates voltage (Seebeck)
  • Coefficients are related: π = T × S

Real-World Applications

Nonequilibrium thermodynamics in everyday life and research

Biological Systems

Living organisms operate far from equilibrium, maintaining complex structures through continuous energy dissipation.

  • Cell metabolism and energy conversion
  • Active transport across membranes
  • Signal transduction and information processing
  • Pattern formation in development

Engineering & Materials

Understanding nonequilibrium processes is crucial for designing efficient systems and novel materials.

  • Heat exchangers and energy conversion
  • Catalyst design and chemical reactors
  • Self-assembly and pattern formation
  • Nonlinear dynamics and control systems

Climate & Environment

Earth's climate system operates far from equilibrium, driven by solar radiation and atmospheric dynamics.

  • Atmospheric circulation patterns
  • Ocean currents and heat transport
  • Weather systems and storm formation
  • Carbon cycle and ecosystem dynamics

Electronic Devices

Modern electronics rely on nonequilibrium processes for functionality and performance.

  • Semiconductor device operation
  • Heat dissipation in processors
  • Thermoelectric cooling and power generation
  • Quantum dot and nanoscale systems

Transportation

Vehicle engines and propulsion systems are classic examples of nonequilibrium thermodynamics.

  • Internal combustion engine cycles
  • Jet and rocket propulsion
  • Hybrid and electric vehicle systems
  • Fuel cell technology