In a new paper (PDF), Richard Littauer, a theoretical physicist at the University of California, Irvine, and Michael Häusser, a physicist at the University of Vienna, take a novel approach to the issue. They have calculated how much energy would be required to keep a system running indefinitely without generating any energy.

In an earlier version of the study (PDF), they proposed a simple energy-generating strategy, based on Gibbs free energy. However, this approach has two issues, both of which they attempt to resolve here.

First, an infinite system is impossible to sustain indefinitely without generating energy—if any energy is even generated. Secondly, the Gibbs free energy method is incompatible with the existence of finite amounts of energy (see the second diagram above). Therefore, Littauer and his coauthors conclude, the simplest and most elegant explanation is to assume that the system has no internal energy, at a minimum. This gives physicists a new and improved way to work with dissipative systems like atoms and molecules.

The system needs no energy to keep going

To find out how much energy it would have to generate to keep the system going indefinitely, Littauer and Häusser first took a look at the energy balance that would happen without any energy at all. They looked at the energy-density profile of the energy and entropy fields of a system at equilibrium and determined that any additional amount of energy would just be passed on to the system.

This is called a dissipative system. It is possible to keep the system in this state indefinitely without making any energy or entropy field changes, even if all the energy and entropy fields are turned off. This means that there is no way for an undisturbed system to generate energy over the entire duration of time on its own without making any change to the system’s energy and entropy fields. The equation for such a system is:

( E ( a ) / E ( b ) ) = ( E ( a ) + E ( b ) )

There is no way to put an upper bound on how much energy this number might be in case this is the final state the system will occupy at some point in time.

Second: This solution doesn’t actually imply the existence of some “equilibrium” energy level (which we do know of, though it’s probably pretty low). This is because the Gibbs free energy estimate just needs to reflect the temperature of the system and the average temperature of the system at a particular time.

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