What is the second part of the declaration of independence

Answer:  Social contract theory

By "the second part," I presume you mean the list of grievances against the British government, which followed the first section (in which natural rights were a strong emphasis).

After asserting natural rights in the opening section, saying that "all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness," then the Declaration of Independence goes on to give a list of "facts to be submitted to a candid world." These facts were meant to demonstrate that the British king had been seeking to establish "an absolute Tyranny over these States" (the colonial states which were declaring their independence).  This was a violation of the social contract which exists between a government and those governed.

The list of grievances against the British government included items such as:

• The king refused to assent to laws that were wholesome and necessary for the public good.
• The king had forbidden colonial governors to enact laws or implement laws without his assent (which, as the prior point noted, he was in no hurry to give).
• The king forced people to give up their rights to legislative assembly or forced legislative bodies to meet in difficult places that imposed hardships on them.
• The king dissolved legislative assemblies and then refused for a long time to have other assemblies elected.
• The king obstructed justice in the colonies and made judges dependent on his will alone for their salaries and their tenure in office.
• The king kept standing armies in place in the colonies in peacetime, without the consent of the colonial legislatures.
• The king imposed taxes without the colonists' consent.

These and additional items listed in the Declaration were meant to support the colonies' position that tyranny was standard operating procedure by the British monarchy, and therefore revolution was justified.  This was based on the idea of the social contract, that a government's authority to govern came from the people, and if the government did not serve the people properly, it could be replaced.   The Declaration asserted that principle in these words:  "When a long train of abuses and usurpations, pursuing invariably the same Object, evinces a design to reduce them [the people] under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security."