### An Introduction to Mechanics

J. W. H., J. P. Clatworthy
1926 Mathematical Gazette
Thermodynamic bodies are being characterized by two competing opposite phenomena, energy and entropy which some researchers in thermodynamics would classify as 'cause' and 'chance' or 'determinancy' and 'random walk', see Müller and Weiss for a nice discussion of both [9] . While at low temperatures energy driven phenomena dominate the body's behavior in terms of mechanical strain energy, stress and strain, the influence of entropy increases significantly with increasing temperature. Think
more » ... biopolymers and biomembranes. When heated up, polymers will no longer rest at a constant position inn space. Rather their individual molecules will move around giving rise to thermal fluctuation. Not only the temperature but also the polymer density in the solution determines the state of a biological substrate. At higher densities, the substrate takes a condensed state of matter and energy dominates its behavior. At lower densities, however, the solution phase is favored in which molecules can move around freely. This state is rather dominated by entropic behavior. To account for both phenomena, it is commont to express the overall free energy ψ as a sum of strain energy W and the entropy S whereby the latter is weighted by the negative absolute temperature T. At a condensed state, the behavior is almost solid like, the strain energy W dominates the response at relatively high density or zero temperature T. At a solute state, the behavior is rather fluid like, the entropy contribution T S dominates at relatively low density or finite temperature T. A transition between phases obviously takes place at ψ = 0, or, equivalently, at W = T S. Remember what Chris said in class about the zero-temperature limit. This does not literally mean that the cell is frozen to zero degrees. Rather it is a common way of expressing that for the particular process we are interested in, the thermal or entropic contribution −T S is negligible as compared to the mechanic contribution W.