Bio-molecules and proteins are building blocks of life as is known, and understanding

their dynamics and functions are necessary to better understand life and improve its

quality. While ergodicity and fluctuation dissipation theorem (FDT) are fundamental

and crucial concepts regarding study of dynamics of systems in equilibrium, biological

function is not possible in equilibrium.

In this work, dynamical and orientational structural crossovers in low-temperature

glycerol are investigated. A sudden and notable increase in the orientational Kirk-

wood factor and the dielectric constant is observed, which appears in the same range

of temperatures that dynamic crossover of translational and rotational dynamics oc-

cur.

Theory and electrochemistry of cytochrome c is also investigated. The seeming

discrepancy in reorganization energies of protein electron transfer produced by atom-

istic simulations and those reported by protein electrochemistry (which are smaller)

is resolved. It is proposed in this thesis that ergodicity breaking results in an effective

reorganization energy (0.57 eV) consistent with experiment.

Ergodicity breaking also affects the iron displacement in heme proteins. A model

for dynamical transition of atomic displacements in proteins is provided. Different

temperatures for rotational and translational crossovers of water molecules are re-

ported, which all are ergodicity breaking transitions depending on the corresponding

observation windows. The comparison with Mössbauer spectroscopy is presented.

Biological function at low temperatures and its termination is also investigated in

this research. Here, it is proposed that ergodicity breaking gives rise to the violation

of the FDT, and this violation is maintained in the entire range of physiological

temperatures for cytochrome c. Below the crossover temperature, the protein returns

to the FDT, which leads to a sudden jump in the activation barrier for electron

itransfer.

Finally the interaction of charges in dielectric materials is discussed. It is shown

that the potential of mean force between ions in polar liquids becomes oscillatory at

short distances.