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Extra info for A new table of seven-place logarithms
We refer here not only to problems of interest for physics and mathematics, but also to a much wider class of problems in different fields such as chemistry, biology, economics, medicine, engineering, social sciences, meteorology, population dynamics and so on. From the viewpoint of computational complexity, the following question naturally arises: can such complex problems be solved efficiently? More precisely, given a generic dynamical system, is it possible Introduction to Classical Computation 31 to find its solution at time t efficiently?
Even though we have a single-molecule system, we may apply the laws of thermodynamics. 36) where dE is the variation of the internal energy of the gas, 5L the work done on the gas and SQ the heat absorbed by the gas. 37) where dS is the variation of the entropy of the gas. Let us assume that our box is in contact with a thermal bath at temperature T and that we compress the gas by means of a frictionless piston (see Fig. 18). 38) where F is the force of the gas on the piston, p its pressure, A the surface of the piston and V the volume of the gas.
We now make a partition of this 32 Principles of Quantum Computation and Information surface, that is, we divide it into a finite set of non-overlapping cells and we identify each cell by means of an integer. If we have perfect knowledge of the system's orbit, we can assign, at time intervals r , the number of the cell in which the system resides. In this way, we obtain a sequence of integers, which provides a coarse-grained description of the orbit. For a chaotic system, no regularity appears.