Strict Entropy Decrease of Clausius Entropy in an Isolated System with Energy-Form Conversion: Theoretical Proof, Numerical Illustration, and Critical Examination

TL;DR

This paper rigorously tests the second law of thermodynamics within Clausius's framework, demonstrating that entropy can decrease in an isolated system with energy conversion, challenging traditional interpretations.

Contribution

It provides a theoretical proof, numerical illustrations, and scope analysis showing entropy decrease in isolated systems with energy-form conversion under Clausius's definition.

Findings

Clausius entropy decreases in ideal energy conversion scenarios

Numerical simulations support the theoretical entropy decrease

The scope analysis clarifies conditions for entropy decrease

Abstract

This paper is accountable only to explicitly stated physical assumptions and strict logical inference. Its goal is to run a rigorous stress test of second-law claims within the Clausius framework. We work directly with \textbf{Clausius's entropy definition} for an isolated composite with energy-form conversion. Heat is withdrawn from a cold releasing subsystem with relatively small heat capacity, converted to electrical energy, and then delivered as heat to a hotter subsystem. In the ideal limit, the electrical leg contributes negligibly to Clausius entropy accounting, so the modeled reservoir Clausius sum is \[ \Delta S_{\mathrm{Cl}} = Q\!\left(\frac{1}{T_B}-\frac{1}{T_A}\right) < 0. \] The paper provides a derivation, numerical illustrations, and a scope analysis; any claimed contradiction should be interpreted as a compatibility issue between different axiom sets, not as an algebraic error in the Clausius bookkeeping above.