Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship

TL;DR

This paper proposes a new information-theoretic framework linking symmetry, similarity, and the Gibbs Paradox, redefining entropy and explaining phase separation without free energy changes.

Contribution

It introduces a novel interpretation of entropy and the Gibbs Paradox based on data compression and information loss, challenging traditional thermodynamic views.

Findings

Gibbs Paradox has been resolved through information theory.

Spontaneous separation of substances is driven by information loss.

No free energy change occurs during ideal mixture processes.

Abstract

Information (I) is defined as the amount of the data after data compression. The first law of information theory: the total amount of data L (the sum of entropy S and information I) of an isolated system remains unchanged. The second law of information theory: Information I of an isolated system decreases to a minimum at equilibrium. The third law of information theory: For a solid structure of perfect symmetry (e.g., a perfect crystal), the information I is zero and the (information theory) entropy (called by me as static entropy for solid state) S is at the maximum. Gibbs Paradox has been resolved. Spontaneously mixed substances at gaseous state can be spontaneously separated at condensed phases (solid or liquid states), driving only by information loss or by the increase in (information theory) entropy. None of the typical pure mixing or separation processes are driving by free energy minimization and the free energy (or total amount of chemical potential) has no change during the processes of ideal mixture formation or ideal mixture separation. The thermodynamic entropy change for the formation of ideal mixtures of gases, liquids or solids is always zero.