This episode is a two-hour deep dive into entropy and the second law of thermodynamics with Professor Wayne Myrvold, who explains that entropy is not a single concept but a family of related but distinct concepts, and that much of what is taught in textbooks—including the popular equation of entropy with disorder—is misleading or outright wrong. The conversation covers the historical origins of thermodynamics as a “resource theory” of heat and work, the difference between Clausius, Boltzmann, and Gibbs entropies, the statistical nature of the second law, Maxwell’s demon, Landauer’s principle, and why the second law cannot be an absolute law if matter is made of molecules.
Thermodynamics began as a resource theory, not a fundamental science
Thermodynamics originated in the 1850s–1860s from practical questions about heat engines: how much useful work can you extract from heat?
Sadi Carnot’s work on heat engine efficiency asked whether the working substance (air, steam, alcohol) mattered; he concluded that maximum efficiency depends only on the temperatures of the heat source and sink, not the substance used.
Kelvin named the field “thermodynamics” from Greek words for heat and power—not “dynamics” in the modern sense of laws of evolution, but literally the science of getting power from heat.
This makes thermodynamics a “resource theory” in modern terms: it asks what agents with certain means and resources can accomplish, not just what physical systems do in isolation.
Clausius coined the word “entropy” in 1865 from a Greek word for transformation, deliberately making it sound like “energy” because he saw it as a closely related concept.
Myrvold argues that if we respected Clausius’s original definition, much confusion would be avoided—but historically, multiple distinct quantities have all been called “entropy.”
The second law does not assume entropy; entropy presupposes the second law
A common statement of the second law is “the total entropy of an isolated system never decreases.” Myrvold argues this is actually backwards: you need the second law first in order to define thermodynamic entropy at all.
Clausius’s approach: consider a cyclic process (like a heat engine) where heat is exchanged at various temperatures. The second law says that if you sum the “equivalence values” of heat transfers (heat divided by temperature, using the absolute Kelvin scale), the total can never be positive—it is zero for reversible processes and negative for irreversible ones.
Only given this second law result can you define entropy differences between two states: pick any reversible process connecting them, sum the equivalence values of heat along the way, and the answer is independent of which reversible path you chose. This independence is a consequence of the second law, not a definition.
If someone truly violated the second law (e.g., moving heat from cold to hot with no other effect), thermodynamic entropy would simply not be well-defined. So “total entropy never decreases” is a consequence of the second law, not the second law itself.
Clausius entropy is independent of molecular hypotheses
Clausius defined thermodynamic entropy purely in terms of macroscopic heat and work exchanges, without committing to any theory about the molecular structure of matter.
Maxwell explicitly said thermodynamics should be neutral about whether matter is made of molecules—it is a science of bulk thermal and dynamical properties.
This is important because it highlights a genuine shift when you move to statistical mechanics: the second law as originally conceived is not strictly true and must be replaced by a statistical version.
The second law is a statistical regularity, not an absolute law
If the kinetic theory of heat is correct (gases are molecules bouncing around), then at a fine enough scale, fluctuations mean you can occasionally get more work out of a heat engine than the Carnot bound would suggest.
You cannot reliably exploit these fluctuations because you are equally likely to get less work. On average, the Carnot bound holds.
Maxwell was the first to clearly articulate this in 1878, calling the second law a “statistical regularity”—analogous to statistical regularities in social sciences (e.g., murder rates per capita in Paris being stable year to year even though individual murders are unpredictable).
The modern view is that the second law is like a gambler trying to break the bank at a casino: occasional wins are possible, but the expectation value is negative, and the law of large numbers guarantees you will not reliably profit.
There are at least two distinct entropies: Boltzmann and Gibbs
Boltzmann entropy is defined by first partitioning the set of possible microstates into macrostates. A macrostate’s entropy is proportional to the logarithm of the number of microstates it contains. It is a property of the macrostate alone and does not depend on what anyone knows about the system.
Gibbs entropy is defined in terms of a probability distribution over possible states. It does depend on what you know (or assume) about the system.
They serve different purposes. Boltzmann entropy tells you something about the system’s physical state. Gibbs entropy is more naturally connected to how much work you can extract, because extractable work depends on what you know and what you can measure.
Arguments about whether entropy is “objective” or “subjective” often arise because people are talking past each other, using different definitions.
The “angel question”: does gaining information change a system’s entropy?
The thought experiment (attributed to Shelly Goldstein): you have a glass of water whose state you know imperfectly. An angel gives you a much better approximation of its state. Has the system’s entropy decreased?
Some physicists say yes—entropy has to do with information, so gaining information changes it. Others say no—entropy is an objective property of the system and cannot depend on what anyone knows.
Myrvold’s resolution: the answer depends on which entropy you mean. If you mean Gibbs entropy (connected to available work), then yes, gaining information can lower it. If you mean Boltzmann entropy (a property of the macrostate), then no.
The deeper issue is whether you conceive of thermodynamics as a resource theory (where knowledge and means of manipulation matter) or as a theory of intrinsic physical properties (where they do not).
Available energy connects entropy to what you can actually do
Available energy (Helmholtz free energy) measures how much work you can extract from a system given a heat bath at a fixed temperature and a required final state.
Available energy depends not just on the physical state of the system but on what you know about it and what means of manipulation you have.
Example: a box of gas has fluctuated so that pressure is higher on one side. If you know which side, you can place a piston and extract work. If you don’t know which side, you might guess wrong and actually have work done on you. The physical state is the same in both cases, but the available energy relative to your knowledge differs.
This is why a notion of entropy connected to available energy should be relative to a state of information—it is non-controversial that extractable work depends on knowledge.
Maxwell’s demon and the cost of erasing information
Maxwell’s demon is a thought experiment: a being that can observe individual molecules and operate a trap door to sort fast molecules one way and slow ones the other, apparently creating a temperature difference without doing work—violating the second law.
Maxwell intended this to illustrate that the second law is a statistical generalization applicable only when dealing with large numbers of molecules in bulk, not when you can manipulate molecules individually.
If the demon must operate in a cycle (returning to its initial state), it cannot reliably violate the second law. In classical mechanics, this follows from Hamiltonian evolution conserving phase space volume. In quantum mechanics, isolated unitary evolution cannot compress a state from a large Hilbert space subspace into a smaller one.
If the demon has a finite memory and must eventually erase its records to continue operating, there is an entropy cost associated with erasure—this is Landauer’s principle. The cost of erasing information exactly compensates for whatever entropy reduction the demon achieved.
If the demon does not operate in a cycle, it is simply consuming a resource (blank memory) and converting it to another resource (a pressure difference)—no violation of the second law.
Macrostates are not fundamental; they depend on what you can measure or care about
A macrostate is a set of microstates grouped together. But the grouping is not given by fundamental physics—it depends on what measurements you can make or what distinctions are relevant to your goals.
One common criterion: a macrostate is a set of microstates indistinguishable by the measurements you will perform. This makes macrostates relative to a set of instruments and their precision.
Another criterion (resource-theoretic): distinctions between states matter only if they make a difference to what you can do with the system. If you can only manipulate bulk properties, then microstate details that don’t affect bulk behavior are irrelevant.
Myrvold argues this is perfectly fine—thermodynamics is not a fundamental theory, and there is nothing wrong with its concepts depending on what we can measure or manipulate.
Entropy is not the same as disorder
There is a rough sense in which entropy correlates with molecular disorder: a gas confined to one side of a box (ordered, low entropy) spreads out (disordered, high entropy).
But the correlation is unreliable. Example: cream poured in coffee forms swirling, turbulent patterns that look disordered, but as it equilibrates to a uniform mixture, it looks simpler and more uniform—yet the uniform state has higher entropy.
When gravity is involved, the relationship reverses: a uniform gas spread through space has lower entropy than the same gas clumped into a star. The clumpy state is intuitively “more ordered” but has higher entropy.
What people sometimes mean by “order/disorder” is closer to “complexity,” which is a different concept: complexity tends to be highest at intermediate entropy, not at minimum or maximum.
The heat death of the universe and whether it matters
Kelvin wrote about a “universal tendency towards dissipation of energy”: eventually, all temperature differences will equilibrate, the sun will burn out, matter will decay into black holes, and no further work will be possible.
This is the “heat death” of the universe. It occurs on timescales of billions to trillions of years.
Myrvold does not find it depressing. Just as individual humans have finite lifespans and should make the best of the time they have, the human species (or its descendants) should make the best of whatever time is available.
On human timescales, there are more pressing concerns than heat death.
Ergodic theory may be irrelevant to statistical mechanics
Ergodicity (classical) means that a system’s trajectory eventually visits every region of its phase space. The quantum analog involves time averages proportional to subspace dimensions.
Some textbooks claim ergodicity is the foundation of statistical mechanics; others say the mathematical results are physically irrelevant.
Myrvold leans toward the latter view: what matters for real systems is what happens on finite timescales (e.g., how long until cream mixes in coffee), not infinite-time averages. Ergodicity results are often about infinite-time behavior and may not tell us anything useful about equilibration in practice.
Statistical mechanics has unresolved foundational issues
Unlike classical electrodynamics (where all textbooks essentially follow a single framework), statistical mechanics textbooks take wildly different approaches, suggesting the foundations are not settled.
Myrvold sees this as evidence that there are genuine unresolved questions about the rationale for standard methods—questions that are often obscured by the textbook tradition presenting everything as worked out.
The field contains different conceptions of what thermodynamics is (resource theory vs. intrinsic property theory) that are rarely made explicit.
Advice for researchers: don’t jump on bandwagons
Myrvold advises against choosing research topics based on what is currently popular or “hot.” If you are not genuinely interested in the work, you will not produce anything compelling, and editors and grant panels are flooded with minor variations on trendy topics.
The opposing vice is choosing something so narrow that only three people in the world can evaluate it. The sweet spot is a topic that some people can engage with but that is relatively unexplored.
As an editor of a philosophy of physics journal, Myrvold found that when a popular book generates dozens of nearly identical submissions, the threshold for publishing any of them becomes extremely high—and an interesting, original project stands out favorably by contrast.
