Second Law of Thermodynamics (2LT)

"Non-equilibrium 'useful energy' (work-potential) is always spontaneously displaced towards mutual equilibrium and dissipated to thermal heat, resulting in irreversible generation of Entropy at every space and time scale (where it can be defined), without exception." -by M.Kostic

Also Entropy Physical Meaning:

More at: Selected Presentations * Proofs of the Fundamental Laws *  Carnot Cycle Efficiency is Fundamentally Misplaced * *** ***

"If Clausius and Kelvin were "fathers of thermodynamics" then Sadi Carnot was the "grandfather" [Kostic, 2023 July 24]or better yet,
Sadi Carnot was the "Forefather of Thermodynamics-to-become" [Kostic, 2023 October 29, and]

NEW:  2024 Key Reflections on the 1824 Sadi Carnot’s Réflexions
* (PDF) * Updated PDF * Back TO> *   E200SCR * CL24 * SCL200

This is Prof. Kostic's Web site being transitioned from the original or Legacy Web(*) - sorry for any broken links referring to it!

NEW: Proofs of the Fundamental Laws: Reasoning and Logical Proofs of the Fundamental Laws: “No Hope” for the Challengers of the Second Law of Thermodynamics by Milivoje Kostic. Entropy 2023, 25(7), 1106; (24 Jul 2023). (Written in popular style FOR EVERYBODY but with deep physical logic and insights for scientists (Philippe Nozieres stated that "only simple qualitative arguments can reveal the fundamental physics”). [Kostic: 2008 & 2011 & 2014 & 2020 & 2023]. 

The Second Law of thermodynamics (2LT) can be challenged, but not violatedEntropy can be decreased locally [by transfer], but not destroyed at any space or time scales. […] The self-forced tendency of displacing nonequilibrium useful-energy towards equilibrium, with its irreversible dissipation to heat, generates entropy, the latter is conserved in ideal, reversible processes, and there is no way to self-create useful-energy from within equilibrium alone, i.e., no way to destroy entropy”. [PFL, 2023], [] (accessed on 22 January 2024). (accessed on 17 January 2024):

Challenge Point A: “Entropy of an isolated, closed system (or universe) is always increasing”, is a necessary but not sufficient condition of the Second law of thermodynamics. Entropy cannot be destroyed (annihilated), locally or at a time, and “compensated” by generation elsewhere or later. It would be equivalent to allowing rivers to spontaneously flow uphill and compensate it with a more downhill flow elsewhere or later. Thermodynamic (macroscopic) entropy is generated everywhere and always, at any scale (where it could be defined) without exception, and it cannot be destroyed by any means at any scale. The impossibility of entropy reduction by destruction should not be confused with a local entropy decrease due to entropy outflow with heat [13,17,18,19,20,21,22].

Challenge Point B: Kelvin's 2LT definition, "A full [100%] conversion of the heat to the work is not possible in a cyclical process [Britannica et al.].", is true [weakly] but not exhaustive (not sufficient/complete): Namely, even a partial conversion of heat to work is not possible if higher than in the corresponding ideal Carnot cycle. Not only 100% of conversion is not possible, but also 75% would not be possible if, for example, heat at 1000K is converted to the work and the remaining 25% transferred to a 300K reservoir, since it is higher than the 70%=1-(300K/1000K) maximum possible conversion by Carnot cycle -- and it would result in violation of the Second Law of Thermodynamics (2LT) with impossible entropy destruction. Note, Clausius' 2LT definition: "A cyclic transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible [Britannica et al.]."

Second Law of Thermodynamics (2LT) - Holistic Reasoning and Generalization: 

It Can Be Challenged, But It Cannot Be Violated! Entropy can be decreased, but cannot be destroyed!

The Second Law of thermodynamics is merely describing “natural-forcing in specific and not in opposite direction, or spontaneous self-tendency of nonequilibrium towards mutual equilibrium”, and impossibility otherwise.

See also Maxwell's Demon Demystified or

Entropy journal - Thermodynamics Section:

       (2023): Reasoning and Logical Proofs of the Fundamental Laws: "No Hope" for the Challengers of the Second Law of Thermodynamics   

       (2022-23):  Special Issue Exploring Fundamentals and Challenges of Heat, Entropy, and the Second Law of Thermodynamics: Honoring Professor Milivoje M. Kostic on the Occasion of His 70th Birthday 

(2020): Topical Collection in Entropy: Foundations and Ubiquity of Classical Thermodynamics

        (2020): Editorial: The Second Law and Entropy Misconceptions Demystified. Entropy 2020, 22, 648 * (OR

Special Issues of Entropy journal edited by Prof. Kostic:

(2018): Nature of Heat and Entropy: Fundamentals and Applications for Diverse and Sustainable Future

(2016): Exploring the Second Law of Thermodynamics

(2013): Entropy and the Second Law of Thermodynamics

See also: Editorial * NIUToday * Dissecting 2ndLaw Challenges [] * Comments to Leff's "Key Points" (G)* PPT-XJTU2019 

The 2nd Law is not about disorder and probability per se (or any other math or physics 'tools' per se used to describe it), but about spontaneous, forced-tendency (natural process-forcing displacement) of mass-energy redistribution in certain, irreversible direction (process driving force), from higher to lower energy-potential (mass-energy density in space). Spontaneity implies forced-directionality and in turn irreversibility. No spontaneous, irreversible process could ever be completely reversed or undone. For example, the driving force for life on Earth is the irreversible dissipation of energy from the Sun.

Challenges to the Second Law Challengers: The 'challengers' need to demonstrate and quantify destruction of entropy to challenge the universal validity of the Second Law. It has been reasoned and thus proven here that destruction of entropy, i.e., violation of the Second Law, is against the forced tendency of natural processes and thus impossible, leaving 'No Hope' for the challengers. After all, the 'Wishful Maxwell's Demon' could not be realized since 1867. [See also arXiv & Harvard and my Comments on Arrow of Time and Common Law of Physics]. After all, before 'the 2nd Law violation' claims are stated, the reliable criteria for the 2nd Law violation, including proper definition and evaluation of entropy, should be established based on full comprehension of the fundamental Laws.

It is hard to believe that a serious scientist nowadays, who truly comprehend the 2nd Law and its essence, would challenge it based on incomplete and elusive facts.

(Thermodynamics is subtle and elusive. Sometimes, highly accomplished scientists in their fields, do not fully comprehend the essence of the 2nd Law of thermodynamics)


The current frenzy about the 2nd Law violation (getting 'useful energy' from within equilibrium alone-PMM2) is in many ways similar to the prior frenzy about the 1st Law violation (getting 'energy' from nowhere-PMM1).

As the fundamental laws of nature and thermodynamics are expanded from simple systems in physics and chemistry, to different space and time scales and to much more complex systems in biology, life, and intelligent processes, there are more challenges to be comprehended and understood.

The perpetual, stationary quasi-equilibrium structures (with bounded non-uniform properties within gravity, electromagnetic or electro-chemical fields) are abundant in nature. As “field-charged bounded structures,” sometimes with elusive work-potential, they may provide limited, transient work only, but not perpetual work to violate the Second Law of thermodynamics, as some are misled to believe. For example, hydrostatic pressure distribution in a container, or adiabatic atmospheric-temperature distribution, or non-uniform distribution of other properties in a stationary equilibrium (like a heated adiabatic-container, compressed container, charged condenser, battery cell, fuel compound, etc.). We called the above a “structural equilibrium” (with non-uniform properties), as opposed to a simple 'ideal thermodynamic equilibrium' (with uniform properties) see Appendix.

A more general statement of the 2nd Law of Thermodynamics could be stated as:

"Non-equilibrium 'useful energy' (work-potential) is always spontaneously displaced towards mutual equilibrium and dissipated to thermal heat, resulting in irreversible generation of Entropy at every space and time scale (where it can be defined), without exception." -by M.Kostic

A consequence of irreversible entropy generation, always and at any scale in general, is a simple special case that entropy is always increased within an isolated system and the universe due to entropy generation, not the other way around.

The Second Law of Thermodynamics is universal and valid without exceptions: in closed and open systems, in equilibrium and non-equilibrium, in inanimate and animate systems -- that is, in all space and time scales useful energy (non-equilibrium work-potential) is dissipated in heat and entropy is generated.

It is critically important to differentiate 'entropy change' (decrease or increase) from 'entropy generation or production': The overall entropy increase, within all interacting systems, due to entropy generation (production), should not be confused with local entropy change that could increase or decrease due to entropy transfer. Entropy may be reduced locally when transferred from a system, but cannot be destroyed by any means, and is always increased within isolated, i.e., all interacting systems, and thus within the universe, due to entropy generation. 'True' entropy is always thermal and universal, since energy is always exchanged in all processes and always dissipated in heat thus generating entropy, and there is no way to destroy entropy.

The Second Law of Thermodynamics (2nd Law) has proved time and again to be universal and valid without exceptions: in closed and open systems, in equilibrium and non-equilibrium, in inanimate and animate systems -- that is, in all space and time scales.  All processes or changes are caused by forced energy transfers where part of useful energy (work potential) is always dissipated to thermal heat accompanied with entropy generation or production, in addition to any entropy transfer with heat transfer.

Only in limit, no entropy generation within ideal reversible processes, where entropy may be transferred and thus conserved, since there is no entropy generation at any space and time scales. However, all real interactions and processes have to be directional (except at equilibrium) and thus at least infinitesimally irreversible with commensurate entropy generation.

Note also that "Arrow of Time" is supposed to be a general concept independent from a clock design or an "observer personal perception," the way Thermodynamic temperature is independent of a thermometer design, or the light speed is independent of an observer speed. The time and entropy are being always irreversibly generated and over-all irreversibly increased. Therefore, the Thermodynamic Arrow of Time, i.e., irreversibility, thus directionality of all processes with entropy generation without exception, may be the answer to "Where Does Our Arrow Of Time Come From? [by Ethan Siegal]." See my related comment: It is premature to make any definitive conclusion about the two before their correlation is well established.

As the fundamental laws of nature and Thermodynamics are expended from simple systems in physics and chemistry, to different space and time scales and to much more complex systems in biology, life and intelligent processes, there are more challenges to be comprehended and understood. For example, on microscopic scale, Thermodynamics becomes Mechanics or Dynamics (i.e., Molecular Dynamics) and the macroscopic, Thermodynamic Laws are not needed nor apply. See my related comments on confusing and misleading article, "The Common Sense Law of Physics: Entropy, Evolution, and Open Systems" by Granville Sewell.

The mass-energy flows at any scale have been, do, and will always and everywhere dissipate energy and generate entropy, as stated by the Second Law, i.e., on the expense of internal and/or surrounding/boundary systems' non-equilibrium. It may appear that the created order or non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the Second Law), due to the lack of proper observations and 'accounting' of all mass-energy flows, the latter maybe in 'stealth' form or undetected rate at our state of technology and comprehension, as the science history has taught us many times (see Challenges to the Second Law Challengers). After all, we have to recognize that natural processes do not obey any law we have defined, but the other way around, our laws describe the natural processes within their limits and simplifications, however, the cause-and-effect, fundamental laws of Thermodynamics are so primitive and appear to be valid without exception, thus universal!

"Nothing occurs locally, nor globally in the universe, without mass-energy exchange/conversion and entropy production. 

It is crystal-clear (to me) that all confusions related to the far-reaching fundamental Laws of Thermodynamics, and especially the Second Law (Abstract & FULL paper), are due to the lack of their genuine and subtle comprehension." > Sadi Carnot's Reflections <*> Clausius Theory of Heat <

 Elusive Nature of Entropy, Nature of Thermal and Mechanical Energy Transfer and Reflections on the Caloric Theory and Thermal Energy. * The Feynman Lectures on Physics

Force or Forcing is a process of exchanging useful-energy (directional, forced mass-energy displacement) with net-zero exchange at forced equilibrium. The Second Law provides conditions and limits for process forcing (energy exchange direction and limit). 

The miracles are until they are comprehended and understood. > Perpetual Motion Machines (PMMs) and The Fundamental Laws of Thermodynamics and Nature*Presentations*Nature of Thermal and Mechanical Energy Transfer*Reflections  and Thermodynamic probability  p=W (Wahrscheinlichkeit, the German word for probability)

Definition of The 2nd Law: The useful-energy (non-equilibrium work potential) cannot be created from within equilibrium alone or otherwise, it only can be transferred between systems (ideally conserved) and irreversibly dissipated towards equilibrium into thermal energy thus generating entropy. Therefore, entropy is transferred and can be reduced (locally) but cannot be destroyed (anywhere): entropy is always and everywhere (locally and integrally) generated or produced.*  dS=dStr+dSgen=dQrev/Tb + dWloss/Tdiss *Irr. Cycle Work Loss*IrRev.Eq. Abstract>Harvard & FULL paper> * Entropy & the 2nd Law Special Issue-PDF>( in NIU Today: Kostic named Guest-Editor of Entropy (png)>&2T

To 'scoop' the useful-energy (for use or storage) require forcing by transferring the useful-energy from elsewhere or even more since in part it will be dissipated (converted) into thermal energy with generation of entropy. It cannot be 'scooped' from within an equilibrium alone nor obtained more than transferred, thus resulting in impossible entropy destruction (i.e., a wishful process without due forcing). Violating the 2nd Law is the same as lifting more weight than appropriate with the �mechanical advantage� lever or superseding �thermal (Carnot) advantage,� i.e., any �energy advantage� device: the useful-energy or work-potential (non-equilibrium) cannot be created but only transferred between, with dissipation (thus partially or fully lost with entropy generation within interacting system/s), and only in ideal limit conserved.* Self-generation of non-equilibrium (work potential), from within an equilibrium or beyond its transfer locally, will amount to self-forcing from nowhere, like self-compression without boundary work transfer (a wishful, boundary self-forcing). A process forcing require transfer of non-equilibrium (the two are cause-and effect, force-flux phenomena) which ideally could be conserved, but is always accompanied with dissipation regardless of the amount (heat & entropy generation, i.e., conversion of other energy types to thermal energy).Entropy cannot be destroyed by any means but is always generated (or produced): Entropy is associated with thermal energy-heat and is generated when heat is generated or irreversibly transferred, otherwise, entropy is transferred and conserved in reversible processes, including reversible heat transfer (at infinitesimally small temperature difference, e.g., ideal Carnot cycles). Even when heat is 'reduced' by conversion to work, the entropy cannot be 'reduced' (destroyed) but is conserved in ideal Carnot and reversible heat engine cycles, and generated during any irreversibility (conversion of any work potential to 'generated' heat). The entropy transfer is equal to reversible heat transfer per absolute temperature since work transfer is not associated with entropy (e.g., reversible compression/expansion); thus, entropy is conserved during reversible processes of any kind (Q/T=S=const), generated due to irreversibility of any kind, and cannot be destroyed by any process (no thermal order), since the latter will imply spontaneous generation of non-equilibrium, including from within equilibrium (e.g., spontaneous heat transfer from cold to hot), thus against the spontaneous forcing. [dS=dStr+dSgen=dQrev/Tb + dWloss/Tdiss ]

*Reflections* See also Entropy Definition *Images>*Reflections *

* Comments to Leff's Key Points * Click HERE for more details

See also Statistical Limitations...