  The holographic principle states that the information about a volume of a
system is encoded on the boundary surface of the volume. Holography appears in
many branches of physics, such as optics, electromagnetism, many-body physics,
quantum gravity, and string theory. Here we show that holography is also an
underlying principle in thermodynamics, a most important foundation of physics.
The thermodynamics of a system is fully determined by its partition function.
We prove that the partition function of a physical system is an analytic
function of all the physical parameters, and therefore its values in any area
on the complex plane of a physical parameter are uniquely determined by its
values along the boundary. The thermodynamic holography has applications in
studying thermodynamics of nano-scale systems (such as molecule engines,
nano-generators and macromolecules) and provides a new approach to many-body
physics.
