# Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $$\partial ^2C/\partial K^2 \geq 0$$, which also means the market implied risk-neutral density is non-negative under no-arbitrage condition, following Breeden-Litzenberger result.

My questions is: is there a way that we could express the calendar spread no-arbitrage conditions in the pdf terms?