Information form of the second law of thermodynamics

TL;DR

This paper proposes a formulation of the second law of thermodynamics based solely on information theory, defining an objective microscopic information entropy and exploring its implications at microscopic scales.

Contribution

It introduces an information-based formulation of the second law, unifying various entropy concepts and clarifying the role of reference frames in entropy definitions.

Findings

Information entropy encompasses Boltzmann, Shannon, and Clausius entropy as special cases.

The observer's reference frame is crucial for defining entropy and understanding paradoxes.

The information second law applies effectively at meso- and microscopic scales.

Abstract

An essential role of information in microscopic thermodynamics (e.g. Maxwell's demon) opens a challenging question if there exists a formulation of the second law of thermodynamics based only on pure information ideas. Here, such a formulation is suggested for unitary processes by introducing information as a full-valuable physical quantity defining an (objective) microscopic information entropy as 'information about microstate'. We show that various forms of entropy (Boltzmann, Shannon, Clausius) are in fact only a special cases of information entropy whose general form is found out. An observer plays here the role of a special (information) reference frame (IRF) towards which the entropy is defined. Some paradoxes or misunderstandings connected with the concept of entropy or the content of the second law arise by describing a situation without specifying a concrete IRF. Typically, the Boltzmann statistical approach cannot be symmetrically used towards the past as towards the future in one IRF. The information second law is full usable at meso- or microscopic scales: the information form of the generalized second law is found out too.