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# The Elusive Nature of Entropy and Its Physical Meaning

Department of Mechanical Engineering, Northern Illinois University, DeKalb, IL 60115, USA

Received: 2 January 2014 / Revised: 10 February 2014 / Accepted: 10 February 2014 / Published: 17 February 2014

(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)

# Abstract

Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased) locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume) of thermal energy due to absolute temperature as a thermal potential (*dQ*

*= TdS*), and thus associated with thermal heat and absolute temperature,

*i.e.*, distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random) thermal energy redistribution (due to heat transfer and/or irreversible heat generation) within a material system structure in space, per absolute temperature level:

*dS = dQ*, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates

_{Sys}/T = mC_{Sys}dT/T*W*(their position and momenta),

*S = k*ln

_{B}*W*, or to the sum of their logarithmic probabilities

*S = −k*ln

_{B}∑p_{i}*p*, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates

_{i}*W*, is correlated with macro-properties temperature

*T*and volume

*V*for ideal gases. A system form and/or functional order or disorder are not (thermal) energy order/disorder and the former is not related to Thermodynamic entropy. Expanding entropy to any type of disorder or information is a source of many misconceptions. Granted, there are certain benefits of simplified statistical descriptions to better comprehend the randomness of thermal motion and related physical quantities, but the limitations should be stated so the generalizations are not overstretched and the real physics overlooked, or worse discredited.

*Keywords:*caloric process; Carnot cycle; Clausius (in)equality; entropy; entropy generation; heat transfer; microstates number; statistical entropy; thermal energy; thermal interactions; thermal motion

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).