A non-equilibrium isolated macroscopic system spontaneously changes into an equilibrium one. The origin of such a well-known thermodynamic phenomenon has been left unclear since the 19th century. This paper shows that irreversible thermodynamic laws can be directly deduced from quantum mechanics if we investigate an isolated system from a new standpoint of looking at it from the inside. This result implies the achievement of a long-awaited target of directly constructing thermodynamic laws from quantum mechanics and leads to the completion of thermodynamics. The result also opens up a new view that diverse macroscopic irreversible phenomena including self-organization and evolution in living organisms can be regarded as macroscopic quantum phenomena and discloses a possibility of producing artificial life and intelligence with a non-mechanical character, for example, those with free will and creativity, through thorough pursuit of an ingenious combination of irreversible processes based on quantum mechanics.
A non-equilibrium isolated macroscopic system spontaneously changes into an equilibrium one. The origin of such a well-known thermodynamic phenomenon has been left unclear since the 19th century. This paper shows that irreversible thermodynamic laws can be directly deduced from quantum mechanics if we investigate an isolated system from a new standpoint of looking at it from the inside. This result implies the achievement of a long-awaited target of directly constructing thermodynamic laws from quantum mechanics and leads to the completion of thermodynamics. The result also opens up a new view that diverse macroscopic irreversible phenomena including self-organization and evolution in living organisms can be regarded as macroscopic quantum phenomena and discloses a possibility of producing artificial life and intelligence with a non-mechanical character, for example, those with free will and creativity, through thorough pursuit of an ingenious combination of irreversible processes based on quantum mechanics.
The law of increase of entropy is one of the most important laws in science but no exact explanation has been given to the origin of it. Statistical thermodynamics only explains it by using Boltzmann’s statistical interpretation together with not sufficiently verified assumptions. This paper shows that the increase of entropy in an isolated macroscopic system can be reasonably explained with no assumption based on quantum mechanics if we take into account that microscopic particles such as electrons and atomic nuclei not only move in space but also have the basic quality of spontaneously spreading into every possible spatial position. The present work allows us to give a plausible definition to the entropy of an isolated system by using the Hamiltonian operator and a wave function of it and provides a firm basis for thermodynamics. It also gives a new physical meaning of entropy effective for further studies of irreversible processes in nature.
The irreversible entropy increase described by the second law of thermodynamics is fundamentally tied to thermalization and the emergence of equilibrium. In the first part of our work (Ref: arXiv.2503.04152), we constructed an isolated gas system model and numerically demonstrated irreversible growth of entanglement entropy caused by erasure of spread non-equilibrium state information. Here, we mathematically prove that for a typical macroscopic system in a non-equilibrium state ∣ϕ0⟩, the quantum state ∣ϕ0′⟩=O^(t)∣ϕ0⟩ will inevitably evolve toward equilibrium. Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective. From this perspective, the second law can be stated as: In typical macroscopic physical systems, the spreading and erasure of non-equilibrium information is inevitable.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
We construct a macroscopic thermodynamical theory that satisfies the second law of thermodynamics, based on quantum mechanics. More concretely, our macroscopic theory satisfies the following two features: (1) A macroscopic equilibrium state is expressed as a set of macroscopic variables a=(a1,⋯,aL), which represents coarse-grained values of a set of physical quantities, and (2) An adiabatic transformation from an equilibrium state a to another state a′ is possible if and only if sa≤sa′ holds. Here, sa is a real-valued function corresponding to the thermodynamical entropy, which depends only on macroscopic variables a. We show that such a macroscopic thermodynamical theory can be consistently constructed if the von-Neumann entropy of a generalized microcanonical state satisfies a generalized central limit theorem. We also show that even when the von-Neumann entropies do not satisfy the condition, a macroscopic thermodynamic-like theory with a similar structure exists, which could be at the foundations of nonequilibrium thermodynamics. Finally, we make a replica of (U,V,N) expression of thermodynamics satisfying (1) and (2), using a toy model of free particles in a box.
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.