We study mutual interplay of information and entropy as
quantum field using an information-theoretic (Shannon entropy)
complex-vector analysis to calculate, respectively, the Gibbs free
energy difference and virial mass. We define conjugate hyperbolic
space and entropic momentum co-ordinates to describe these
spiral structures in Minkowski space-time, enabling a consistent
and holographic Hamiltonian-Lagrangian system that is completely
isomorphic and complementary to that of conventional kinematics.
Such double spirals therefore obey a maximum-entropy pathintegral
variational calculus (“the principle of least exertion”. These
simple analytical calculations are quantitative examples of the
application of the Second Law of Thermodynamics as expressed in
entropy terms. They are underpinned by a comprehensive entropic
action (“exertion”) principle based upon Boltzmann’s constant as
the quantum of exertion.