9.23 Non-equilibrium Thermodynamics
409
environment). If an energy flow through the system is maintained, the system may
be able to continue its ordering of subsystems, producing complexity in contained
structures.
An adiabatic process that involves the transfer of energy from one form to
another without a redistribution of the particles among possible energy states,
is non-dissipative and non-entropy producing. For example, an electric motor
need not produce heat, transferring 100% of electric field energy into coherent
mechanical motion. As the flagella motors on bacterial cell walls are partly electric
motors, running on proton currents, their efficiency is only partly restricted by
thermodynamics.
9.23 Non-equilibrium Thermodynamics
9.23.1 Near-Equilibrium
Near equilibrium, thermodynamic variables for a system with a large number of
particles, such as temperature, pressure, and chemical potential, are still measurable,
with relatively small fluctuations. Those changes in a closed system which increase
its entropy are called dissipative. 67
Now consider how the entropy changes when a system is near but not at
equilibrium. We start with non-dissipative processes in a closed system, for which
T dS = dE + pdV −
i
μ i dN i ,
(9.238)
showing how the internal entropy changes when any of the extensive variables
E, V , {N i } change. The relation for the entropy has the form
dS =
1
T
dE +
p
T
dV −
i
μ i
T
dN i .
(9.239)
67 Dissipative changes allow us to deduce the direction of time. People sometimes laugh when
viewing a film run backward. We do not expect to see balls bounce higher by themselves, or warm
water turn to steam and ice. But the electromagnetic interactions which accurately describe the
microscopic behavior of atoms and molecules are symmetric under time reversal. (Experimentally,
the decays of kaon particles show a non-time reversal behavior, but this decay is not governed
by Maxwellian electromagnetic interactions.) The loss of time reversal symmetry we observe
in macroscopic processes comes from energy being dispersed among the available multitude of
microstates, with little chance of this process reversing. Discrete models of nature could allow
the information to be cryptically stored, so that the entropy produced is a measure of our lack of
practical access to that information. In quantum language, wave functions would not ‘collapse’
during an observation, but rather the wave function for a macrosystem and a macroscopic observer
would become entangled and in many circumstances the changes are practically irreversible.
409
environment). If an energy flow through the system is maintained, the system may
be able to continue its ordering of subsystems, producing complexity in contained
structures.
An adiabatic process that involves the transfer of energy from one form to
another without a redistribution of the particles among possible energy states,
is non-dissipative and non-entropy producing. For example, an electric motor
need not produce heat, transferring 100% of electric field energy into coherent
mechanical motion. As the flagella motors on bacterial cell walls are partly electric
motors, running on proton currents, their efficiency is only partly restricted by
thermodynamics.
9.23 Non-equilibrium Thermodynamics
9.23.1 Near-Equilibrium
Near equilibrium, thermodynamic variables for a system with a large number of
particles, such as temperature, pressure, and chemical potential, are still measurable,
with relatively small fluctuations. Those changes in a closed system which increase
its entropy are called dissipative. 67
Now consider how the entropy changes when a system is near but not at
equilibrium. We start with non-dissipative processes in a closed system, for which
T dS = dE + pdV −
i
μ i dN i ,
(9.238)
showing how the internal entropy changes when any of the extensive variables
E, V , {N i } change. The relation for the entropy has the form
dS =
1
T
dE +
p
T
dV −
i
μ i
T
dN i .
(9.239)
67 Dissipative changes allow us to deduce the direction of time. People sometimes laugh when
viewing a film run backward. We do not expect to see balls bounce higher by themselves, or warm
water turn to steam and ice. But the electromagnetic interactions which accurately describe the
microscopic behavior of atoms and molecules are symmetric under time reversal. (Experimentally,
the decays of kaon particles show a non-time reversal behavior, but this decay is not governed
by Maxwellian electromagnetic interactions.) The loss of time reversal symmetry we observe
in macroscopic processes comes from energy being dispersed among the available multitude of
microstates, with little chance of this process reversing. Discrete models of nature could allow
the information to be cryptically stored, so that the entropy produced is a measure of our lack of
practical access to that information. In quantum language, wave functions would not ‘collapse’
during an observation, but rather the wave function for a macrosystem and a macroscopic observer
would become entangled and in many circumstances the changes are practically irreversible.