Physical Foundations of Landauer's Principle

We review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and proper interpretation remain frequently misunderstood. Contrary to some misinterpretations of the Principle, the mere transfer of entropy between computational and non-computational subsystems can occur in a thermodynamically reversible way without increasing total entropy. However, Landauer's Principle is not about general entropy transfers; rather, it more specifically concerns the ejection of (all or part of) some correlated information from a controlled, digital form (e.g., a computed bit) to an uncontrolled, non-computational form, i.e., as part of a thermal environment. Any uncontrolled thermal system will, by definition, continually re-randomize the physical information in its thermal state, from our perspective as observers who cannot predict the exact dynamical evolution of the microstates of such environments. Thus, any correlations involving information that is ejected into and subsequently thermalized by the environment will be lost from our perspective, resulting directly in an irreversible increase in total entropy. Avoiding the ejection and thermalization of correlated computational information motivates the reversible computing paradigm, although the requirements for computations to be thermodynamically reversible are less restrictive than frequently described, particularly in the case of stochastic computational operations. There are interesting possibilities for the design of computational processes that utilize stochastic, many-to-one computational operations while nevertheless avoiding net entropy increase that remain to be fully explored.Comment: 42 pages, 15 figures, extended postprint of a paper published in the 10th Conf. on Reversible Computation (RC18), Leicester, UK, Sep. 201

Landauer's principle and divergenceless dynamical systems

Landauer's principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that "information is physical". Landauer's principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.Facultad de Ciencias Exacta

Landauer's principle and divergenceless dynamical systems

Landauer's principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that "information is physical". Landauer's principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.Facultad de Ciencias Exacta

Operational Thermodynamics from Purity (extended abstract)

This is an extended abstract based on the preprint arXiv:1608.04459. We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms 'Causality, Purity Preservation, Pure Sharpness, and Purification' identify purity as a fundamental ingredient for every sensible theory of thermodynamics. Indeed, in physical theories satisfying these axioms, called sharp theories with purification, every mixed state can be modelled as the marginal of a pure entangled state, and every unsharp measurement can be modelled as a sharp measurement on a composite system. We show that these theories support a well-behaved notion of entropy and of Gibbs states, by which one can derive Landauer's principle. We show that in sharp theories with purification some bipartite states can have negative conditional entropy, and we construct an operational protocol exploiting this feature to overcome Landauer's principlepublished_or_final_versio

Theoretical Setting of Inner Reversible Quantum Measurements

We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a unitary transformation on the state of the closed quantum system by means of a collection of generalized measurement operators. In particular, given a complete set of orthogonal projectors, it is possible to implement a reversible quantum measurement that preserves the probabilities. In this context, we introduce the concept of "Truth-Observable", which is the physical counterpart of an inner logical truth.Comment: 11 pages. More concise, shortened version for submission to journal. References adde

The Information Catastrophe

Currently we produce 10 to power 21 digital bits of information annually on Earth. Assuming 20 percent annual growth rate, we estimate that 350 years from now, the number of bits produced will exceed the number of all atoms on Earth, or 10 to power 50. After 250 years, the power required to sustain this digital production will exceed 18.5 TW, or the total planetary power consumption today, and 500 years from now the digital content will account for more than half of the Earths mass, according to the mass energy information equivalence principle. Besides the existing global challenges such as climate, environment, population, food, health, energy and security, our estimates here point to another singularity event for our planet, called the Information Catastrophe.Comment: 4 page