The second law of thermodynamics

The second law is the origin of both the origin of the asymmetry between past and future and the origin for the existence of thermodynamic equilibrium in mechanical systems.

There four forms of the second law in model systems, one of these forms is the particular form observed in reality.

SL-I

for all t.

In this case the entropy is constant, there is no asymmetry between past and future and there is no thermodynamic equilibrium.

SL-II

for all t>t'

This form has an asymmetry between past and future, but does not guarantee that the entropy will converge.

SL-III

for all t>t'
This form has an asymmetry between past and future and the entropy converges. This is enough to guarantee that the system will evolve towards equilibrium, however, the entropy and thus the equilibrium may depend on the initial state.

SL-IV

for all t>t'

This form has an asymmetry between past and future and the system evolves towards an equilibrium state, which is independent of the initial state.

SL-IV is the form of the second law observed in thermodynamics.

Much of the following discussion evolves around the investigation of which modification to Hamiltonian dynamics is required to change the second law for the system from SL-I to SL-IV.

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Author Per Stoltze stoltze@fysik.dtu.dk