What is the physical meaning of negative resistance?
There are a number of mechanisms that result in a region where locally increasing voltage results in locally decreasing current. For example, an Esaki (tunnel) diode. 



A common example would be a switching power supply with a steady load. Assuming the efficiency is more-or-less constant, increasing the input voltage results in less current being drawn. It is always consuming energy though.  

A stand-alone component that exhibits negative resistance (rather than negative differential resistance) is not possible without some kind of energy source within the component, otherwise it would violate conservation of energy (\$P = E^2/R\$) and negative P would indicate it is acting as a power source. 



If  you want to play with a negative resistance effect, one way (assuming you don't mind one end being grounded) is to use a negative impedance converter: 







simulate this circuit &ndash; Schematic created using CircuitLab

The above circuit acts like a -10K resistor with one end grounded (within its linear range), and works down to about zero volts. Any power it produces comes from the op-amp supplies.