Nozick's objection to Rawls' 'difference principle' is that it is a patterned principle. This means that it considers, without regard to how actual distributions of property or entitlements ('goods' for short) have come about, that there is a proper or just pattern of distribution. That is, a pattern in which 'Social and economic inequalities are to be arranged so that they are ... to the greatest benefit of the least advantaged'.
This is clean contrary to Nozick's idea of how just distributions come about. For Nozick property holdings or entitlements are just depending purely on how they have been initially acquired and how they have been subsequently transferred. (This is why he calls his theory a historical entitlement theory of just distribution : how a distribution of goods has come about is decisive.) There are conditions for just acquisition and conditions for just transfer; as long as these conditions are met, whatever distribution of goods results is just.
It is fairly evident that there is no guarantee or even likelihood that a specific preferred pattern of distribution of goods - one that satisfies the difference principle - will result from the the processes of just acquisition and just transfer that Nozick specifies. It might do - but I might win the lottery. There can be certainty or even probability.
To complete the story we should note Nozick's slogan, 'liberty upsets patterns'. To create a distribution that fulfils the difference principle, there will need to be redistribution. This will be unjust since it removes from those with just holdings of goods (by Nozick's criteria) what is justly theirs. More than that, once the redistribution has taken place, the pattern of distribution dictated by the difference principle can be preserved only by limiting or removing people's ability justly to acquire and to transfer and so upset the pattern. That is, by curtailing their liberty.
Robert Nozick (Contemporary Philosophy in Focus)
ISBN 10: 0521006716 / ISBN 13: 9780521006712
Published by Cambridge University Press, 2010.
Santosh Bakaya, The Political Theory of Robert Nozick,
ISBN 10: 8178354810 / ISBN 13: 9788178354811
Published by Gyan Books, India, 2006.
A.R. Lacey, Robert Nozick,
ISBN 10: 0691090440 ISBN 13: 9780691090443
Published by Princeton University Press (2001).
Simon A. Hailwood, Exploring Nozick: Beyond Anarchy, State and Utopia (Avebury Series in Philosophy).
ISBN 10: 185972485X / ISBN 13: 9781859724859.
Published by Averbury, 1996.
Jonathan Wolff, Robert Nozick: Property, Justice, and the Minimal State,
Published by Cambridge : Polity Press, 1991*
*Copies may be hard to find but this is an exceptionally lucid introduction to Nozick.
Pulin B. Nayak, 'Nozick's Entitlement Theory and Distributive Justice', Economic and Political Weekly, Vol. 24, No. 4 (Jan. 28, 1989), pp. PE2-PE5+PE7-PE8.
Neil Cooper, 'Justice and Historical Entitlement', Canadian Journal of Philosophy, Vol. 7, No. 4 (Dec., 1977), pp. 799-803
Thomas Scanlon, 'Nozick on Rights, Liberty, and Property', Philosophy & Public Affairs, Vol. 6, No. 1 (Autumn, 1976), pp. 3-25.