Abstract

In this letter, it is argued that the correct counting of microstates is obtained from the very beginning when using Newtonian rather than Laplacian state functions, because the former are intrinsically permutation invariant.

Highlights

  • In this letter, it is argued that the correct counting of microstates is obtained from the very beginning when using Newtonian rather than Laplacian state functions, because the former are intrinsically permutation invariant

  • The paradox consists in that the Lagrange-Laplacian notion of state does predict a change in entropy, because it counts the interchange of two “identical” particles as representing two different states—at variance with the experimental outcome and with Gibbs’ writing quoted above. This situation suggests to seek a state description, where the state is not changed by the opening of the valve above

  • The state description should be invariant against the interchange of equal bodies

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Summary

Introduction

It is argued that the correct counting of microstates is obtained from the very beginning when using Newtonian rather than Laplacian state functions, because the former are intrinsically permutation invariant. Consider the classical mixing entropy, in particular the following case of “two identical fluid masses in contiguous chambers” The paradox consists in that the Lagrange-Laplacian notion of state (comprising the dynamical variables positions and velocities or momenta of all bodies involved [2]) does predict a change in entropy, because it counts the interchange of two “identical” particles as representing two different states—at variance with the experimental outcome and with Gibbs’ writing quoted above. This situation suggests to seek a state description, where the state is not changed by the opening of the valve above.

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