# Could time (or space) discretisation be needed in order to preserve the law of increase of entropy?

+ 0 like - 0 dislike
75 views

In Introductory Statistical Mechanics, 2nd Edition, by R. Bowley and M. Sanchez, pages 81-83 is given a proof of the second law of thermodynamics by showing that the probability of a system being in a state described by an energy 20 standard deviations away from the mean (which is the energy corresponding to the maximum value of entropy) is so small that even considering that the system is in a different microstate every 10-50  seconds would yield approximately one such state every 1038 seconds (which is practically never).

My question is what stops us from considering that the system is sampling a different microstate every, say, 10-1000 seconds, provided that time and space are considered continuous variables? In this case the probabilities would have unreasonable values for the system being in a state in which the entropy would be much lower than its maximum possible value. One way of saving this argument could be that either time or space (or both) could be discrete so that no system could change its microstate faster than a given amount of time (which could depend on the system's microscopic parameters such as the number of particles). Is this a necessary assumption in order to keep the argument valid?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.