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Complex Systems: Far-from-equilibrium Thermodynamic Systems

Review Article

An extensive and technically accessible overview of the field.


Since its origin in the nineteenth century, the science of thermodynamics has been concerned with the transformations of energy and its unavoidable dissipation into heat according to thermodynamics’ first (conservation) and second (entropy) laws. Also since its inception, thermodynamics has focused on phenomena taking place at or near equilibrium in energetically isolated systems. A new development occurred however in the second half of the twentieth century with the rise of far-from-equilibrium thermodynamics, especially through the pioneering work of Ilya Prigogine (Nobel Prize 1977) on the evolution of dissipative structures in systems open to energy fluxes.

These structures are characterized by:

  • nonlinearity
  • the existence of bifurcation points
  • the local creation of order out of disorder, and
  • the formation of complex systems

Examples include:

  • convection currents in fluids
  • turbulent flow
  • snowflakes
  • hurricanes
  • and most biological phenomena

Additional Works

Some current treatments with extensive bibliographies: