Thermodynamics Lite

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Thermodynamics Lite
New improved!
More refreshing!
Less filling!
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Recommended books(now on reserve)

• Kondepudi, D. K. Prigogine, I. 1998. Modern
  thermodynamics from heat engines to dissipative
  structures.
• Assumes some mathematical background.
• Some parts assume familiarity with the basic
  principles of thermodynamics
• Includes material directly relevant to course
  topics (e.g. self-organization)

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Thermodynamics and self-organization

• Key concepts
• Equilibrium and nonequilibrium thermodynamics
• Linear and nonlinear thermodynamics
• Dissipative systems

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Extremum principles

• It is a general observation in many areas of
  physics that natural phenomena occur in such a
  way that some physical quantity is maximized or
  minimized, or in general terms, extremized.
• Examples
• Soap bubbles minimize surface area
• Light traveling through different media takes the
  path that minimizes the travel time

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• In thermodynamics, one basic extremum principle
  is the 2nd law
• isolated systems go to the equilibrium state in
  which the system's entropy is maximized, and its
  rate of entropy production is minimized.
• Another is that in closed systems the free energy
  tends to be minimized.

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• But, not all systems (or even most natural
  systems) are isolated.
• Unlike isolated systems, open systems may be kept
  far from equilibrium indefinitely by the flow of
  energy or matter through them.

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Equilibria

• No system is ever perfectly static in a given
  state, due to
• External perturbations from outside the system
  (imperfect isolation.
• Internal fluctuations (e.g. random movement of
  atoms due to heat.)

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• Equilibria are states that are inherently stable
  despite perturbations or fluctuations.
• As long as a system is near its equilibrium
  state, after any small deviation, it will
  naturally tend to return to equilibrium because
  of the thermodynamic extremum principles.

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• Chemical reactions do not go entirely to
  completion but rather to a state of dynamic
  equilibrium where adding or removing the
  slightest amount of reactant or product will
  cause a shift in the direction of the process (E.
  g., they are reversible
• E.g.
• A B ? C
• C ? A B
• Equilibrium A B ? C

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• For example If temperature is initially not
  uniform in a system, heat will flow until the
  entire system reaches a state of uniform
  temperature the state of thermal equilibrium
• All isolated systems inexorably move toward, and
  then remain at, thermal equilibrium.
• More generally, if a physical system is isolated,
  its state moves irreversibly towards a
  time-invariant state in which no further change
  occurs in any macroscopic variable. This is the
  state of thermodynamic equilibrium, which
  includes thermal equilibrium
• The evolution of a system toward equilibrium is
  caused by irreversible processes. At equilibrium,
  these processes cease.
• Thus, a nonequilibrium state can be described as
  one in which irreversible processes are driving
  the system toward equilibrium.

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• Systems that are near thermodynamic equilibrium
  are in the linear regime, meaning that the
  thermodynamic flows are linear functions of the
  thermodynamic forces.

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Far-from-equilibrium systems

• In Nature, isolated systems are rare, and
  far-from equilibrium systems are ubiquitous.
• The earth is an open system subject to the
  constant flow of energy from the sun.
• Every form of life lives only through the flow of
  energy and matter.

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Open Systems

• Although isolated systems move inexorably toward
  thermodynamic equilibrium, in open systems the
  flow of energy and matter through the system can
  drive it and keep it far from equilibrium.

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Far-From-Equilibrium Systems

• The rules are different for far-from-equilibriu
  m systems.
• Far-from-equilibrium systems are in the
  nonlinear regime, meaning that the
  thermodynamic flows are nonlinear functions of
  the thermodynamic forces. Consequently
• For far-from-equilibrium systems, there are no
  general extremum principles that predict the
  state it will move toward.
• They can change unpredictably as a result of
  random fluctuations, perturbations or other
  random factors such as inhomogeneities or
  imperfections, the system can evolve to any one
  of many possible states.
• Which it will evolve to is generally not
  predictable.
• The new states thus attained often possess
  spatiotemporal organization.

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• It is particularly easy to create nonlinear
  systems of chemical reactions, for example
  through the positive feedback of autocatalysis.
• E.g. A B ? C D,
• where D catalyzes the reaction.
• Nonequilibrium chemical systems, in combination
  with diffusion, can produce ordered phenomena
  such as oscillating concentrations, traveling
  waves, and geometrical concentration patterns

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Dissipative Structure

• A system that exists far from thermodynamic
  equilibrium, hence efficiently dissipates the
  heat generated to sustain it, and has the
  capacity of changing to higher levels of
  orderliness. According to Prigogine, systems
  contain subsystems that continuously fluctuate.
  At times a single fluctuation or a combination of
  them may become so magnified by possible
  feedback, that it shatters the preexisting
  organization. At such revolutionary moments or
  "bifurcation points", it is impossible to
  determine in advance whether the system will
  disintegrate into "chaos" or leap to a new, more
  differentiated, higher level of "order". The
  latter case defines dissipative structures so
  termed because they need more energy to sustain
  them than the simpler structures they replace and
  are limited in growth by the amount of heat they
  are able to disperse.
• - From the Web Dictionary of Cybernetics and
  Systems

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• Self-organization is generally restricted to
  dissipative structures.
• Dissipative Structures do not violate the second
  law because they increase external entropy (by
  dissipating heat) at greater rate than they
  decrease internal entropy.

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The end.