Energy, Entropy and Information on D. Lairez

The principles of neopositivism and the laws of thermodynamics

Mon, 01 Jun 2026 00:00:00 +0000

The second law of thermodynamics, which deals with irreversibility and makes the theory so special, is usually considered empirical. The definition of equilibrium as an attractor, on the other hand, requires a postulate. This article shows that both are actually already contained, even if hidden, in the fundamental principles of neopositivism, which are widely accepted in all fields of science. In particular, from the definition of information as a truth that can only come from an observation but cannot be redundant, we obtain Clausius’ inequality.

Disentangling Brillouin's negentropy law of information and Landauer's law on data erasure

Mon, 01 Dec 2025 00:00:00 +0000

The link between information and energy introduces the observer and his knowledge into the understanding of a fundamental quantity of physics. Two approaches compete to account for this link, Brillouin’s negentropy law of information and Landauer’s law on data erasure, which are often confused. The first, based on the Clausius’ inequality and Shannon’s mathematical results is very robust, while the second, based on the simple idea that information needs a material embodiment (data-bits) is today perceived as more physical and prevails.

Energy and information: a chronicle of hesitations on the role of the observer in physics

Sun, 25 May 2025 00:00:00 +0000

Energy has no definition, except that given by a conservation principle which essentially amounts to defining it as the elements of an open list of unknown cardinality. Entropy, identified by Shannon as information we lack, has too many definitions. This results in an unstable and hesitant interpretation of their link.

Thermodynamics, the science of changes in form of energy, is phenomenological, all its laws are induced from observation. From the origin, the concept of energy is linked to the observer’s knowledge, to the information he has: what and where to look and with what instruments. Thermodynamics only addresses the sensible world. It is Aristotelian. But this is disturbing if we consider that reason can give us access to Plato’s intelligible world, the one that is beyond the sensible world and independent of us. This is disturbing if we consider that science can access to the intrinsic properties of things, those which are independent of us. This is disturbing if we have a purely Platonic conception of science. Hence the statistical mechanics approach (“The rational foundation of thermodynamics”, J.W. Gibbs). This is the first pendulum movement of ideas, whose oscillations continue to this day, because unfortunately statistical mechanics introduces many inconsistencies, mainly due to the ergodic hypothesis. Luckily, these inconsistencies are all solved by Shannon’s information theory. Sadly, information theory is too Aristotelian and too conceptual. Fortunately, Landauer principle makes it more \textquote{physical}. This is currently the latest attempt to bringing the notions of energy and information back to what is considered the right side of science, that of Plato. Landauer principle is now commonly regarded as a fundamental law of physics. Unpleasantly, it can be shown that this principle is not one.

The fundamental difference between Boolean logic and thermodynamic irreversibilities, or, why Landauer's result cannot be a physical principle

Fri, 29 Nov 2024 00:00:00 +0000

Landauer’s “principle” claims that erasing one bit of information necessarily dissipates at least Tln2 of heat into the surroundings, making a possibly logically irreversible Boolean operation also thermodynamically irreversible. It is commonly accepted that this result is a fundamental principle of physics that definitively establishes the link between information and energy. Here, we show that this result cannot be general. In fact it comes (1) from a confusion between logical and thermodynamic irreversibilities and between logical and thermodynamic states, which is reminiscent of the classic Gibbs paradox about the joining of two volumes of the same gas, and (2) from two unnecessary constraints imposed on the erase procedure. Clarifying these points permits us to dissociate the two irreversibilities; to invalidate Landauer’s result as being a general physical principle; and to open the door to hardware implementations allowing erasure to follow a thermodynamically reversible, or at least quasistatic, path.

Thermostatistics, information, subjectivity, why is this association so disturbing?

Sat, 11 May 2024 00:00:00 +0000

Although information theory resolves inconsistencies (known under the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This is interpreted as being mainly due to epistemological rather than scientific reasons: the subjectivity introduced into physics is perceived as a problem. This paper attempts to expose and clarify where exactly this subjectivity lies: in the representation of the reality and in probabilistic inference. Two aspects which have been integrated into the practice of science for a long time and which should no longer frighten anyone, but which become explicit with information theory.

On the supposed mass of entropy and that of information

Mon, 15 Apr 2024 00:00:00 +0000

In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. Potential energy of a body is actually stored under the form of rest mass, interaction energy too, temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence the “mass-energy-information equivalence principle” that has been recently proposed.

In this paper, it is first recalled that for a thermodynamic system made of non interacting entities at constant temperature, the internal energy is also constant. So that, the energy involved in a variation of entropy (T ΔS) differs from a change in potential energy stored or released and cannot be associated to a corresponding variation of mass of the system, even if it is expressed in term of quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state dependent property) and thermodynamical irreversibility (a path dependent property) and to return to the nature of the link between energy and information that is dynamical.

Thermodynamical versus logical irreversibility : a concrete objection to Landauer's principle

Tue, 01 Aug 2023 00:00:00 +0000

Landauer’s principle states that the logical irreversibility of an operation, such as erasing one bit, whatever its physical implementation, necessarily implies its thermodynamical irreversibility.

In this paper, a very simple counterexample of physical implementation (that uses a two-to-one relation between logic and thermodynamic states) is given that allows to erase one bit in a thermodynamical quasistatic manner (i.e. that may tend to be reversible if slowed down enough).

Two-to-one implementation of a bit inspired by my practice of bicycles: the two bit-values correspond to one single thermodynamic state. Erasing the bit (setting it to 0) is necessarily thermodynamically reversible.

Plea for the use of the exact Stirling formula in statistical mechanics

Fri, 17 Feb 2023 00:00:00 +0000

In statistical mechanics, the generally called Stirling approximation for N! is actually an approximation of Stirling’s formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirling’s exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbs’ paradox of joining two volumes of identical gas. This amendment clearly results in a gain in consistency and rigor of these solutions.

A short derivation of Boltzmann distribution and Gibbs entropy formula from the fundamental postulate

Fri, 03 Feb 2023 00:00:00 +0000

Introducing the Boltzmann distribution very early in a statistical thermodynamics course (in the spirit of Feynmann) has many didactic advantages, in particular that of easily deriving the Gibbs entropy formula. In this note, a short derivation is proposed from the fundamental postulate of statistical mechanics and basics calculations accessible to undergraduate students.

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What entropy really is : the contribution of information theory

Fri, 21 Oct 2022 00:00:00 +0000

Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to embrace it. However, it is pointed out that the lack of coherence of certain presentations or certain preconceived ideas do not help. They are of three kinds : 1. axiomatic thermodynamics; 2. inconsistent solutions of certain paradoxes; 3. reluctance of physicists to the simplification provided by information theory. The purpose of this paper is to examine these points in a didactic way by paying attention to the structure of the theory, what are the foundations, how ideas articulate, with a peculiar focus on their consistency and economy. It is shown how entropy can be introduced in a more consistent and economical manner with the help of information theory, which from the start takes into account its subjective nature, finally allowing a more intuitive understanding.