II 262
Order/Genz: when everything has decayed to dust, the remaining order of atoms and molecules is still "infinitely" much larger than the disassembled one.
II 263
Definition micro-state/gas/Genz: a micro-state is the state of the entirety of molecules (location and speed of molecules). Different micro-states are compatible with the same macro-state.
The larger the volume of a gas, the greater the number of possible micro-states.
Order: therefore, a smaller gas volume is always in a more orderly state than a larger one.
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Entropy.
II 264
Order/temperature/Genz: analogous to this applies here: the higher the temperature, the greater the number of possible speeds of individual molecules.
Definition Entropy/measure/disorder: entropy is the number of possible micro-states of a macroscopic object that are compatible with a given macro-state of that object.
Problem:
1. the micro-states of quantum mechanical objects are quite different.
2. for counting the states, discrete values must then be assigned to the continuous variables.
Since the number is very large, you do not use them yourself, but the number of digits that would require you to write them down.
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Quantum mechanics.
II 266ff
Probability/micro-state/gas/Genz: it is so unlikely that all molecules will come together once in the left half of the container and leave the right half empty that it will not occur in world ages. This is a physical "never" or "always", not a mathematical one.
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Probability.
II 268
Explanation/general/Genz: general explanations do not refer to certain bodies. They say that all developments always lead from improbable to probable conditions.
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Explanations.
Impossibility/physical/Genz: unlike the mathematical impossibility: is the highest improbability. For example, it is impossible to set an initial state that would cause all molecules to assemble on the left side of the box because it is undetectably isolated in a continuum of states that have no such consequence.
II 310
Order/realism/idealism/descartes/Leibniz/Spinoza/Genz: thesis: the "identity of ideal and real order of things" is based on a common ground of both.
Descartes/Spinoza: this is the work of God as a creator of both the world and the cognitive mind.
Leibniz: the pre-stabilized harmony.
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G.W. Leibniz, >
B. Spinoza.
II 326
Order/disorder/entropy/Turing machine/Genz: it is an important question how entropy as a measure can be freed from the arbitrarily chosen size of the assumed fields in a Turing maschine.
In fact, it is not only the location of the particles that is required to define entropy, but also the simultaneous indication of location and velocity in a phase space. However, the uncertainty ratio applies to both together.
Solution: therefore, entropy can be traced back to the division of phase space into boxes with volumes as small as is compatible with the blur of location and velocity.
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Uncertainty principle.
