Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

Mass measurements of some proton-rich nuclei

The Q values and 0^o cross sections of (He³, n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si²⁶ (85), S³⁰ (-573), Ar³⁴ (-759), Ti⁴² (-2865), Cr⁴⁸ (5550), Ni⁵⁶ (4513) and Zn⁶⁰ (818). At least one excited state was found for all but Ti⁴². The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He³, p) Q values of reactions leading to V⁴⁸, Co⁵⁶, and Cu⁶⁰. Many excited states were seen: V⁴⁸ (3), Co⁵⁶ (15), Cu⁶⁰ (23). The first two states of S³⁰ are probably 0⁺ and 2⁺ from (He³, n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar³⁴ (measured ^Ƭ1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe⁵⁴(He³, nγ)Ni⁵⁶. Possible collective structure in Ni⁵⁶ and Ca⁴⁰, both doubly magic, is discussed.

The (He³, n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si²⁸ (n, α) Mg²⁵ and Si²⁸ (n, p) Al²⁸, are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg²⁵ and Al²⁸ ions are discussed. The 0^o cross section for Be⁹ (α, n) C¹², used to provide calibration neutrons, has been measured with a stilbene spectrometer for n_o (5.0 ≤ E_α ≤ 12 MeV), n₁ (4.3 ≤ E_α ≤ 12.0 MeV) and n₂ (6.0 ≤ E_α ≤ 10.1 MeV). Resonances seen in the n_o yield may correspond to nine new levels in C¹³.

The reduced-alpha-width of the lowest 1¯ state of ^(16)O

Cross sections for the reaction ¹²C(α,γ)¹⁶O have been measured for a range of center-of-mass alpha particle energies extending from 1.72 MeV to 2.94 MeV. Two 8"x5" NaI (Tℓ) crystals were used to detect gamma rays; time-of-flight technique was employed to suppress cosmic ray background and background due to neutrons arising mainly from the ¹³C(α,n)¹⁶O reaction. Angular distributions were measured at center-of-mass alpha energies of 2.18, 2.42, 2.56 and 2.83 MeV. Upper limits were placed on the amount of radiation cascading through the 6.92 or 7.12-MeV states in ¹⁶O. By means of theoretical fits to the measured electric dipole component of the total cross section, in which interference between the 1¯ states in ¹⁶O at 7.12 MeV and at 9.60 MeV is taken into account, it is possible to extract the dimensionless, reduced-alpha-width of the 7.12-MeV state in ¹⁶O. A three-level R-matrix parameterization of the data yields the width Θ_α,F² = 0.14^+0.10_-0.08. A "hybrid" R-matrix-optical-model parameterization yields Θ_α,F² = 0.11^+0.11_-0.07. This quantity is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.