  Electrical heat engines driven by the Johnson-Nyquist noise of resistors are
introduced. They utilize Coulomb's law and the fluctuation-dissipation theorem
of statistical physics that is the reverse phenomenon of heat dissipation in a
resistor. No steams, gases, liquids, photons, combustion, phase transition, or
exhaust/pollution are present here. In these engines, instead of heat
reservoirs, cylinders, pistons and valves, resistors, capacitors and switches
are the building elements. For the best performance, a large number of parallel
engines must be integrated to run in a synchronized fashion and the
characteristic size of the elementary engine must be at the 10 nanometers
scale. At room temperature, in the most idealistic case, a two-dimensional
ensemble of engines of 25 nanometer characteristic size integrated on a 2.5x2.5
cm silicon wafer with 12 Celsius temperature difference between the warm-source
and the cold-sink would produce a specific power of about 0.4 Watt. Regular and
coherent (correlated-cylinder states) versions are shown and both of them can
work in either four-stroke or two-stroke modes. The coherent engines have
properties that correspond to coherent quantum heat engines without the
presence of quantum coherence. In the idealistic case, all these engines have
Carnot efficiency, which is the highest possible efficiency of any heat engine,
without violating the second law of thermodynamics.
